Here is some general information to help get started on learning the run. It's probably going to turn into a rambling mess halfway through.
DISCLAIMER: The following notes are specifically for the Story Mode Easy category. Not all things mentioned here apply to Medium and Hard difficulty.
-Bunny-hopping. It's Shaq's fastest mode of travel when he's not holding a weapon. Basically, hit jump before landing and the delay of Shaq's landing animation disappears.
-Weapons in this game each have a set amount of times they can be used before breaking. Even if you swing and hit nothing, that counts as a use. Most weapons are extremely useful as they can knock out grunts in a single shot and have a wide swing to hit multiple attackers. Also, ones that are part of the environment will respawn after a set amount of time. Just don't get knocked down or knocked out of the air or the weapon will break.
-If you want to get rid of a weapon, like when a screen is cleared and you need to move to the next one, just Shaq Smash and the charge will instantly break the weapon.
-The biggest time sink across the entire run is Shaq's tendency to do mini-cutscene kills where the camera zooms in and he knocks someone out in slow motion. Each time this happens it adds a few seconds to your time. These only happen to the generic grunts for each stage and their slightly stronger variants, like the soda zombies in Baby's Crib or the soldiers that grow in size in Fiji. Also, these can trigger even if the enemy has full health. There are a few ways to avoid these:
-The Size 22 attack comes in four different varieties, depending on when in Shaq's combo you use it:
-Shaq's combos allow for a slight delay between each attack. By that I mean you could, say, throw two punches, take a moment to move into position, then keep attacking and you'll be on the third attack in the combo. Combo buffering comes in handy to, for example, build up to the roundhouse Size 22 as enemies are still making their way on screen so you can knock most of them out immediately.
-Shaq Diesel sections. Just hold punch all the time. Even if you're not hitting anything, you'll build up the heat meter and, by extension, be able to use multiple Shaq Waves at a time. A bell rings three times when you're about to overheat (when the meter is completely full)... most of the time. If too many sounds are going on at once, sometimes the bell noise won't play.
-Shaqtus sections. Shaq has two attacks in this mode: throwing needles and throwing red needles with the Size 22 button. The red needles will hit and fly through all enemies in their path, so they're handy for when multiple stronger enemies show up at once.
-In some cases, enemies can be hit before they're even on screen. Take for example the Shaq Diesel sections. When enemies are jumping in from off-screen, technically their hitbox appears before they do, so a well-timed Shaq Wave can cause them to instantly appear and die.
-You start every stage with a full Shaq Wave meter, allowing for two Shaq Wave uses. Don't be afraid to use them early on; it will build back up pretty fast.
Now for some stage-specific notes.
STAGE 1 - Hunglow
-Be careful after the first enemy encounter. If you get the mini-cutscene kill on the last enemy and immediately start jumping right, you'll bypass a couple enemy encounters. That's good, except those encounters are needed to unlock the Shaq Smash and Size 22 attacks. This is an instant reset.
-Missiles drop at certain points. Since they're based on where you're standing, these can be aimed into groups of enemies on either side of the screen.
-MINI BOSS: Frizzle
-NOT A MINI BOSS: Shappy
STAGE 2 - Baby's Crib
-The Devotees will summon a few extra enemies if they finish their cheering animation, so it's best to deal with them ASAP.
-Soda zombies have an anti-air attack, so be careful if you're jumping from one side of the screen to the other.
-Soda on the ground can cause Shaq to slip when using the Shaq Slam.
-Mall cops will counter any Size 22 attacks, but are susceptible to everything else. I try to group them up with a Shaq Slam and Shaq Wave them if it's available.
-After busting down the gates, walk through them and immediately walk all the way to the bottom of the screen, then bunny-hop to the right. You'll pass a limo and some idle enemies. Closely walk around the pillar and move forward normally. Congratulations! You skipped an enemy encounter and a mini boss!
-Sugar Slingers can be used to your favor. When you get close to them, they'll fire a charged red shot all the way across the screen which can damage other enemies. Also, this causes a button prompt to appear which can deal extra damage to them and stun them for a bit. for this section though, it's better to use the barrel to the upper left whenever it appears.
-Regular grunts hit by the Sugar Slinger's ranged attack will turn into soda zombies, another reason to make sure they only use their close-range attack.
STAGE 3 - Sunset Strip
-Lipstick Lizards, moreso than their other variants, can be easily stunlocked by using the one-attack Size 22 attack over and over. This can come in handy if you don't have a weapon and they keep jumping out of the way of other attacks.
-Motorcycle guys can be dealth with a few different ways. If you're behind them you can do a button prompt to one-hit kill them. A Size 22 attack also works. Or, if you want to take out several at once, a well-placed Shaq Wave can knock off several of them at once. The motorcycle guys have generous hitboxes for the Shaq Wave and can be hit by it even a second or so after it goes off.
-After the cutscene in the bar, throw a punch before picking up the barrels. For some reason the game might not let you grab them if you don't.
STAGE 4 - Bel Air
-The lawyer's ranged attack is a fireball, which Shaq can catch and throw back across the screen, damaging every other enemy in its path and stunning the lawyer. Handy for when the lawyer and a group of enemies are on opposite sides of the screen.
-MINI BOSS: Chang
-Beware of cars. Leading enemies into their path can help slow them down, but oddly don't do much damage compared to Shaq's fists. It's good for keeping the groupies from summoning more enemies though.
-I'm sorry, what?
-Use any Shaq Waves immediately. When the fight gets going with Kandy's special attack, you won't have much use for them.
-In a nutshell, do as much damage as possible to induce her Brownbeard's Cannon attack. When she does this, jump kick her over and over. On Easy the fire won't do enough damage to Shaq for you to worry about not getting hit. Do the button prompt when it shows up and, when she gets back up, she'll go right back into the special attack. Jump kick until dead.
STAGE 5 - Fiji
-Once the blue glowing soldiers grow to full size, they become immune to the Shaq Smash. Get them while they're normal sized or use other attacks.
-In groups, the Fiends are the enemies I go for first. After a couple attacks they use an electrified whip which stuns Shaq for a few seconds.
-Neros, even while floating in the air, can be hit with Shaq Waves and weapons. However, you have to wait until they bob down closer to the ground. Barring that, a jump kick will knock them down.
-After the bridge, taking too long at the next screen can lead to missile carpet bombing almost the entire area.
-Hooligans are absolute damage sponges, but being close to them causes a counter prompt to appear which takes off about a third of their health.
-After the Shaqtus section, the mines roll down the hill according to your position. Slightly moving side to side is enough to not get hit. It's possible to time jumps so you clear the mines without doing so, but the window for it is pretty tight.
-The mine-rolling sections are agony. Keep rolling the mines as soon as they pop up as enemies spawn and walk in from off-screen. Take out any enemies that spawn at the top of the hill ASAP to help shorten the length of each screen. Also, don't try jumping ahead of the mines to grab health or power meter blobs from below. If Shaq lands on or gets hit by a mine he started rolling, it's a one-hit kill.
STAGE 6 - Hell
-Not much I can add about the stage proper, except in the Shaqtus section when two portals pop up at the same time, just use a red spine to destroy both of them in one go. The same goes for the Shaq Diesel section when three portals appear; hop in the middle and use a Shaq Wave.
-BOSS: Yen Lo Wang
RANDOM EXTRA THING
Just adding a couple notes here after my most recent runs: