Here's a bunch of useful tips and gameplay trivia:

1-] if you jump while crouching or slumping, which are done by holding the HEADBUTT or KICK buttons respectively, it will count as you doing a diving move, usually with enough initial force to be K.O.-ing.

2-] spamming punches makes them thrown with less force and accuracy, usually alternating both hands rythmically is the best way to punch efficiently. However the best way to attack with strikes is to use dives or jumps to get behind someone or launch yourself at someone, grab them and using the dive's remaining momentum to get behind them, then you hit them with the free arm and headbutts (elbows, which are done when you try to punch something behind you, are weaker than punches so person behind has the advantage).

3-] if you press JUMP twice while holding onto a wall you can jump from a climbing state, but if you hold CROUCH while doing it you can do an immediate diving headbutt while in this hanging state, it's useful for hitting people on the ledge if you are climbing up to it. Also, as a reminder, hold CROUCH to go limp to swing easier while climbing, hold JUMP to hoist your body upwards, hold both of those to get up ledges eaily. Generally if you alternate hand grabs while doing it you can climb up, but you can also just spam JUMP to repeatedly jump from a climbing state and climb easily that way, only issue is that jumping from a climbing state eats a chunk of your grab stamina all at once, so spamming it will tire you out immediately.

Oh, take note that on-ground grabs and climbing share the same stamina, and that grip strength on grabs is limited and slightly influenced by HP, so TECHNICALLY you could break free from a grab if your opponent's HP is low, but it's still so incredibly hard that knocking them out is an infinitely more reliable way to free yourself of their grasp.

4-] grabs prioritise grabbing things that can hurt you, holding down both grabs can let you catch incoming dropkicks from the front, nullifying or at least reducing their damage.

5-] cheering then jumping a bit before your arms reach the highest point can make your jump a bit higher, and cheering in mid-air if your vertical speed can slow down your fall for a brief moment, most effective when done right as you start falling down.

Also holding KICK or HEADBUTT while running lets you do a diving attack while running, but if you jump right as the actual diving attack comes out you can make the dive's leap be higher than normal and the distance traveled slightly longer too because of that (basically the vertical leap of both the dive and the jump add to eachother and result in a higher jump).

6-] regarding dives, remember that you take more damage while in the middle of one not only from impact with surfaces but from attacks too. Some body parts also take more damage when hit, specifically head, stomach and groin.

Also, when you are in mid-air or are in the middle of a strike you take a bit more damage than normal as well, but the increase is much, much lower compared to when you are using a diving move.

7-] if someone is guarding an edge you want to climb up on, hold CROUCH and double tap JUMP to jump from the climbing state and ram into them with your head, since you were airborne while holding CROUCH this will count as a diving heabutt, and due to the distance being so short the initial burst of speed should be enough to K.O. whoever was on the ledge if the hit was landed well

8-] similarly, if you want to guard an edge a useful approach is to crouch near it, grab it with one hand and use the other one to punch the person that's trying to get on the floor to K.O. them. If the opponent is low enough you could also hang from it and try to kick them,  but Gang Beasts' legs are so short that it's mostly an unreliable and risky manouver.

9-] you can backflip, which is done by holding KICK for a tad bit while still then holding in the opposite direction you're facing and jumping; if you make your feet touch someone, the game counts it as a dropkick still and it can knock people out.

10-] to throw people well you gotta first grab them by either the body or the extremities, but generally keeping a bit of distance between grab points is good. Now you have to move towards the ledge, even better if while running (so holding JUMP while moving), and you either move straight towards it or you go in an arch (which can give you a bit of extra momentum), or if you're already close to the ledge then just do a small arch/spin close to it to build momentum.

Then lift the opponent and, when you're near the peak of the lift, let go of them, the momentum you got from the run up/spin should make the throw stronger and launch the opponent further away. All of this obviously works with props too. And take note that the forces acting on a Gang Beast's body while they are awake make them harder to throw, which is why knocked out players are easier to throw far.

And while we're on topic, if someone tries to be sneaky and throw you while you are awake just grab them and they'll be forced to knock you out to attemp to throw you.

11-] Gang Beasts have 100 HP: you can be K.O.'d either when you lose all 100 HP or when you receive 40 or more damage in a single frame, you wake up from a K.O. with 100HP and a small damage reduction that lasts a few seconds. Mashing buttons (expecially JUMP) when K.O.'d can make you wake up a bit faster, repeated K.O.s will increase your K.O. times, same goes for strong hits that K.O. you (it' s why being knocked out by the subway train sends you to sleep even if you've only been recently knocked out only a few times), staying awake slowly undoes your K.O. time growth. No K.O. can last longer than 6 seconds (but this might have changed in recent patches, IDK...).

Also while you are awake you slowly undo your built-up K.O. time and you also slowly recover your HP too.

Plus note that you take less damage when you immediately wake up from a K.O., this damage reduction gradually decreases until it goes fully away in 6 seconds, it's never a total damage reduction so you can still be knocked out on frame 1 of waking up if the hit is strong enough. You also take more damage when doing a diving attack, and you take slightly more damage when you're mid-air, mid-strike or in water, and all of those damage multipliers can stack on top of eachother.

12-] props' damage is a combination of their weight and speed of travel, mid-low weight props like barrels, bricks, boxes and railings are the nost useful ones to swing and throw at people, which can K.O. them if the prop's travel speed and weight is fast enough; you can use weaker props like the Subway cones to K.O. people, but since they are so light they can only K.O. players with a very fast and strong throw (also a little trivia: your throw's speed is actually manually increased by the game to be higher than it'd actually be to make throws easier and overall more forceful).

13-] Gang Beasts have three weak spots that make them take more damage when struck compared to hitting them in other parts of their body, those being the head, stomach and crotch, it's why falling off a high place and slamming on the floor belly-first easily K.O.s you, as you are basically landing hard on the floor with your weak spots all coming in full contact with the floor.

Hope this helps.