Seeing how complicated the guide is, here's my recommendation in a summary:
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Dealing Damage:
Beginner strat: Up Smash. Just spam up smash.
Advanced strat: Alternate between Full-Hop Fair-Nair and Full-Hop Fair-Uair.
The advanced strat is only faster if you can perform the double aerial with over 50% consistency. If you can't, then stick to Up Smash.
Regardless of the strat you use, whenever Master Hand is not able to be hit, charge a Giant Punch. When it is fully charged, use it immediately (so that you can charge it again if necessary)
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Finishing off Master hand:
Up-B: 12% damage (comes out on frame 3 and has a large hitbox) Up Smash: 21% damage if advanced strat used (16% if beginner strat used due to stale moves). Fully Charged Giant Punch: 36% damage
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For more detailed information, or for more situational strats and stuff, read below, but the summary above should be more than enough unless you're going for a fully optimized time.
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For beginners, use Up Smash. It's the easiest consistent strategy. What I'm going to describe below is a complex sequence that is only faster if you can perform it consistently (i.e. over 50% of attempts are successes). Conveniently, 50% is basically the "borderline" between which is faster. But if you're not comfortable performing double aerials (fairly precise sequence), then stick to Up Smash.
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The strategy I am describing is using a full hop, then performing two aerials within that Full Hop. The first is a Forward Aerial (aka Fair), while the second could be any of the others, as I'll describe below. The timing is fairly precise, but something that can be practiced to a good level of consistency. This strat is significantly faster than only using Up-Smash, so if you are able to perform it, I highly recommend it.
When I refer to frames of leniency, I mean the number of frames that you can "drop", or "not put an input", and still be able to perform the sequence. A 0 frame leniency means that you must be frame perfect on the whole thing, while a 5 frame leniency means you can "miss" up to 5 frames (so basically a 6 frame window).
All my leniencies are assuming a neutral C button full jump (neutral stick position during the startup of the jump). Doing a fully angled C button full jump (holding hard left or right) loses 6 frames of leniency on the cycle, meaning that a 9 frame leniency is now a 3 frame leniency, etc. Also, doing a max height stick jump increases leniency by one frame (this may depend on the controller, as different controllers have different max height stick jumps). So if you're using a different jump method, or accidentally do an angled C jump, then you'll have to take that into account.
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For every double aerial cycle, the ideal situation is to start with Fair, and then a second aerial on the descent before you land. Doing Fair-Fair cycles are ineffective, as you're permanently using a stale Fair, and are only dealing 12 damage per hit (compared to using Fair every second move, where Fair deals 14 damage, a 2 damage increase plus an increase depending on the other move)
Looking at the other 2nd aerials aside from Fair (for reasons above), the highest damage aerials are Nair and Bair, both dealing 15% fresh. Fair-Nair has 9 frames of leniency, while Fair-Bair has 5 frames of leniency. So using Fair-Nair cycles is the most DPS option with the highest leniency. The other thing about Nair is that the only other aerial, Uair, has only one extra frame of leniency while dealing only 12 damage fresh (or 3 damage fewer at every level of staleness). So it's fairly clear that Fair-Nair is the best single string to use.
For all these cycles, Fair as the first aerial is going to deal 14 damage, so I'll only look into the second aerial. I'm also going to be putting values in terms of two cycles (i.e. Fair-Nair-Fair-?air).
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If Nair is the only aerial used, it will be on the second worst level of staleness, dealing 13 damage total. So doing Fair-Nair only means the second aerial is doing 13 damage each time. In a 2 cycle string (Fair Nair Fair Nair), this will deal 26 damage for the second aerials total. Both cycles have 9 frames of leniency.
If we alternate Fair-Nair with a different second aerial (i.e. Fair-Uair, Fair-Dair, or Fair-Bair), Nair's damage dealt will be the same damage as its "fresh" damage output (15%). The move isn't technically "fresh", but the way the damage calculation is done, it rounds up to 15% damage dealt. So that means that in a two cycle string (Fair Nair Fair ?air), the Nair will deal 2 damage more than if we were to only use Fair Nair. The other aerial used will also deal damage equivalent to its "fresh" state (i.e. damage rounds up to its fresh amount).
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The other three aerials all have results that are better than only using Nair as the second aerial, but each have different damages and leniencies (conveniently, the higher the damage, the smaller the frame leniency and therefore the harder it is to perform). From easiest to hardest:
Uair: 12% damage, 10 frames of leniency. Fair-Nair-Fair-Uair deals 1 damage more than Fair-Nair alone, with Uair having more leniency. Therefore, Fair-Nair-Fair-Uair is better than Fair-Nair alone. For the other two aerials, we'll use Uair as the base case (i.e. Fair-Nair-Fair-Uair).
Dair: 13% damage, 7 frames of leniency. Fair-Nair-Fair-Dair deals 1 damage more than the Uair version, but has 3 fewer frames of leniency.
Bair: 15% damage, 5 frames of leniency. Fair-Nair-Fair-Bair deals 3 damage more than the Uair version, but has 5 fewer frames of leniency. For completion's sake, Bair deals 2 damage more than the Dair version, but has 2 fewer frames of leniency.
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For the sake of full damage numbers and a convenient to read format:
Fair-Nair-Fair-Nair: 54 damage, leniencies of 9 and 9 (including for completion's sake, but do not use this) Fair-Nair-Fair-Uair: 55 damage, leniencies of 9 and 10 Fair-Nair-Fair-Dair: 56 damage, leniencies of 9 and 7 Fair-Nair-Fair-Bair: 58 damage, leniencies of 9 and 5
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So the best strategy is to use Fair-Nair-Fair-?air, where the last aerial depends on how consistent you are, or how risky you feel like being (or how many frames of leniency you feel you have remaining when using the last aerial). Keep in mind that if you have lost "frames of leniency" before performing your last aerial, those should be taken into account when deciding which aerial to use. For example, if you do an angled c button jump, the leniency decreases by 6, meaning Uair has 4 frames of leniency, Dair has 1, and Bair is impossible (TAS is one frame late). Also, if your Fair does not come out immediately after jumping, and comes out a little late, then you are losing frames of leniency from that as well. So if the startup leading to the second aerial is poor, then an easier second aerial should be used to ensure that the move does connect. If you know you're losing frames of leniency, and are panicking on which aerial to use, just use Uair, as it's the easiest/safest one. Ensuring you hit the aerial is far more important than the minor damage decrease you would get for using a different aerial. Note: This applies to the Fair-Nair as well that starts the 4 aerial sequence. Uair has one more frame of leniency than Nair, so if you feel you're losing too many frames on the startup of the cycle, then use Uair, and then use Nair on the cycle after that and continue on.
So based on that info, it's your choice on whether you want to use Uair, Dair, or Bair as the last aerial in the second cycle. That said, missing one aerial due to using a more complex cycle is slower than getting a perfect with an easier cycle. So make sure that you use the cycle you feel the most comfortable with.
Also note that the actual damage difference in the fight as a whole is rather minimal. Dair only ends up dealing 4-5 damage more than Uair during the course of the entire fight, while Bair deals 8-10 damage more than Dair (and 12-15 damage more than Uair). So the reward you get for using a harder strat is very minimal compared to the risk involved in using that strat. Whether you use the best strat (Bair) or worst strat (Uair) will either result in no difference at all, or one extra move needed (less than a second), so taking that into account, it may be better just to stick to Uair, as the risk of using other strats is not entirely worth the reward you get. That said, if Master Hand runs away from you at 2HP and uses a gun move, then that strat difference will make a huge impact (as a better strat would have KO'd before Master Hand runs away), but barring some event like that, the Uair variant would be the one I would recommend.
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If you cannot perform full hop double aerials with over 50% consistency, then ignore all of this. Up Smash is the easier and more consistent strat. Double aerials only deal more DPS if you can perform them with more than 50% consistency. So if you either aren't consistent, or are too nervous to do them properly (or are scared of choking away a good run), stick to Up Smash. If you are able to perform double aerial, then I highly recommend doing that.
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Other things to consider:
When Master Hand is using an attack, but is vulnerable during the attack, attack him with the best move you can use in that situation. If Master Hand is using an attack from the background (giving you one attack to use), these are the best moves to use: Giant Punch deals 36 damage, Up Smash deals 21 damage, F-smash deals 20 damage (21 if angled up), Down smash deals 19 damage. Down smash is the easiest to land, so if you don't know the timings of the others, I'd say stick to down smash.
If Master hand uses the fist punch from above, only attack him if you have time to dodge and/or shield the attack before it hits you. While getting that extra bit of damage is good, being knocked away and delaying your double aerial cycles is not worth it.
If Master hand is using the double poke move, continue doing double aerials until he's about to attack, then dodge the attack.
If Master Hand is doing the walk across the stage move, end it as soon as possible, as the sooner it ends, the sooner you can continue double aerials. However, make sure you don't get launched away, or you're losing time.
Anytime Master Hand does an attack which you can't punish (e.g. guns), charge punch as much as possible. A fully charged punch deals 36 damage. As soon as it's charged, use it on him as soon as possible (don't wait). The only exception to this is if you are going to KO him this cycle before he runs off, in which use it as a finisher as soon as his HP is 36 or below.
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Finishing moves at various percents:
12 HP and below: Up-B (frame 3, ground and air) 13 HP: up-tilt (frame 4) 14-19 HP: Down Smash (frame 12) 20-21 HP: Up Smash (frame 16) Up to 36 HP: Neutral B (frame 23, ground and air, only if fully charged)
These values are from after landing from a double aerial, or if Master Hand finishes a move. Basically, it assumes you're on the ground.
If you're in the air, most likely it is from starting a double aerial, and are between aerials at the given percentages. In this case:
12 HP and below: Up-B (frame 3) 13-15 HP: Bair (frame 8, the damage assumes Bair is fresh. Double jump into a Bair if necessary) 16-36 HP: Giant Punch (frame 23)
If you're in the air at 16HP or higher, and don't have a fully charged punch, then finish the double aerial (use Nair instead of Uair or Dair if they were the next move you'd use, as Nair deals more damage than Uair, while it deals the same damage as Dair with a higher frame leniency). Then use the ground finisher that matches the HP shown by Master Hand.
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This is a lot of information (it turns out DK on Master Hand is a lot more complicated than everyone thought). If you don't want to think about numbers and math and such, just use Fair-Nair-Fair-Uair, then either Up B at 12HP or lower, or Giant Punch at 36HP or lower if fully charged. If you're panicking and are not able to think of what to do properly, and need to fall back on something, fall back on that, as it's basically the "safe" version of this strat, and is basically just as fast as nearly any other optimization shown above. If you're completely panicking, and are struggling with getting double aerials down entirely, stick to Up Smash, and then finish with up-B when he's at 12HP or lower.
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I might make a video guide of this, as considering how complex this is, a visual representation may be a better way to explain it, and to show what is going on. Otherwise, I hope this helps, and good luck on your runs.
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