I will write some things here to help you to beat these bosses mabye a bit easier. This will mostly be strategies for speedrunning ofcourse.

Very long post

Disclaimer: These are my strats, you can find something else helps for you.

You can go to: https://hearthstone.gamepedia.com/Book_of_Heroes for more info about the decks.

Archmage Antonidas

This is a tricky one to speedrun. Mainly because the deck you get is not all that great and Mirror Image from Antonidas.

There are 2 strategies: 1: Don't kill the Mirror Image tokens 2: (obviously) kill the tokens (Although it's not worth it, No further explination) 3: No Mirror Image is played ( Play minions, and hope for the best, No further explination)

Main goal: Antonidas's board full of Mirror Image tokens. Play minions with stats and hit face with spells in the meantime, play flamestrike and go face.

Get a Antonidas's board full with Mirror Image's, so he wouldn't play any other minions. He can do this with: 2x Mirror Image or Echo of Medivh or Molten Reflection. When his board is full he will waste his Freezing Potion and Molten Reflection. And He will likely play Research Project, which will benefit you the most.

Now that his board is full: Play minions with stats. The best would be Gray Cats, Water Elementals and Animated Avalanche. Play a Water Elemental on 6 mana so the effect of Animated Avalanche will be active on turn 7. If you cannot play a minion that turn, hit face with frostbolt or fireball. When you have enough damage to kill him with your minions play Flamestrike and kill him.

Dead Cards: Animated Broomstick, Voracious Reader, Mirror Entity, Flame Ward, Polymorph (Icicle, counterspell, Archmage, Stormwind Champion)

Good Cards: Gray cat, Water Elemental, Animated Avalanche, Flamestrike, (frostbolt, fireball)

Keal'Thas

This is a run killer for sure. 
He has a lot of clear, can make his board big in a turn with Wyrm Weaver and his heropower doesn't really help you to accomplish your goals.

Main Goal: Play defensively. play minions when you can (MINIONS ARE KEY, your minions have to do the most face damage), hope that your minions don't die, slowly kill him.

Turn 2: ping Fire Fly, if not played, face.
Turn 3: Ping Starscyer if played Otherwise Gray Cat, Counterspell or Arcane Intellect.
Next turns really depends on what he plays. Try to keep the board stable and play your minions effectively, so they stay alive and can do some face damage.

His treatening minions are: Mana Wyrm, Firebrand, WyrmWeaver and Dalaran Mage (spell damage is scary when it's too late)

Dead Cards: Potion of Illusion, Luna's Pocket Galaxy (Ice Block)

Good Cards: (keep: Deep Freeze) ALL MINIONS, counterspell, iceball, frostbolt, draw, frost nova, blizzard, ray of frost, deep freeze.

Prince Arthas

Not too big of a deal

Main Goal: Get him below 10HP and finish him of with a pyroblast. or play a lot op spells so you can play both arcane giants.

His heropower: He will always use heropower when you have a minion on board, most of the time he will use it at the start of his turn, so making it's effect useless.

Your heropower: 2 mana deal 3 damage. This is very good to kill his minions and ping face with.

Kill his minions if needed, ALWAYS KILL PARAGON OF LIGHT. Do damage face, ALWAYS use heropower instead of spells. use Tortollan Pilgrim as draw, secret or boardclear. At the end play Siamat with windfury or some Arcane Giants to go face with. He has a lot of heal, but you should have enough burst left to burn him down. his secret is always Noble Sacrifice.

All cards are decent, but the worst are defenitly Sorcerer's Apprentice and Luna's Pocket Galaxy.

Grommash Hellscream

Easy as pie

It is possible to kill Grommash before Thrall's dialogue starts, but it will most likely not happen in a speedrun

Use heropower every turn you can and you win, you can just go face.
For the first 3 turns you try to get Fireball, frost nova or sorcerer's Apprentice

Archimonde

This is a kind of a weird one. This one has a lot of 'rules' applied

• Boss always has 1-2 mana minions in his starting hand and always draws Voidwalker on turn 1.
• The player always draws the cards on first six turn in next order - Ray of Frost, Frostbolt, Flame Ward, Fireball, Blizzard, Frost Nova. If any of these spells were got on mulligan, the player will draw a random card instead on respective turn. The spells above may be one of these randomly drawed cards which leads to another random draw on turns 1-6 accordingly.
• The battle ends with the player winning when Archimonde's health reaches 10 or less.

So you don't have to do anything during the muligan, these cards are all you need. Same with Grommash: use heropower every time you can, or something else must be better.

Garrosh Hellscream

Gosh darn pirate warriors!

Again press that heropower!
Muligan for Kirin Tor Elemental, Arcane Missiles, Archmage Kalec, scalerider, (scaleworm)
Trade at the start. (you can choose not to, but it can happen that you lose)

Thrall

Should be easy, but may be slow

You need to kill his minions, because of his windfury heropower. Your heropower will help inmensely with this. He has mostly big elemental minions

This is another defensive game. For the early game try to get: Kirin Tor Elemental, Archmage Kalec, Violet Spellwing, Scalerider and Scaleworm. Focusing Iris is defenitly the best card, but it usually gets counterd by Earthquake. Thrall doesn't really have many minions till turn 5 so play your minions and go face. Save your spells for when you really need them.

Aethas Sunreaver

First pirate warrior and now secret mage!?

Again play defensively and make an opening to play minions and attack.
He has 3 different kind of secets: Counterspell, Explosive Runes and Flameward.
Kill his secret synergising minions, Stargazer Luna and Wyrm Weaver.
Archmage Kalec is a minion that needs to survive, he is great playing the bigger spells like: pyroblast, Luna's Pocket Galaxy, flamestrike, meteor or just some fireballs from Staff of Antonidas.

When he plays Aluneth, your goal will be to play Arcane Giant and Violet Warden so he won't do any face damage with the minions. You can let him draw his whole deck and kill him with fatigue, but that is very slow. Just use your Pyroblast and Fireball to burn him down.

His heropower is almost useless and his Sunreaver Warmage is just a 5 mana 4-4, because he doesn't have any spells that cost 5 or more.


I hope this helped. If you have any tips yourself, feel free to post them below.
You can always go to: https://hearthstone.gamepedia.com/Book_of_Heroes for more info on the decks.