I finally got the speedrun.com page for Paprium all set up, which will hopefully encourage people to submit times for the game. It's quite niche given its availability and exclusivity to the console, so by all means, submit a run to the boards (no matter how bad you think you are at it).
I'm a speedrunner, but I'm not particularly good at brawler speedruns. They involve a lot of spawn management and crowd control. I imagine there's still a lot of tech to discover since the game is quite massive from a scale standpoint. That said, here's what seems to work for me.
Jump kick. It hits 3 times in the air, is active all the way to the ground in most circumstances, and does a ton of damage to stunned enemies. Ba Ba has the best, followed by L. Ektra, then maybe Alex and Dice are next best.
Tug and Spinal are just kind of bad in general. Their jump kicks have trouble hitting stunned enemies since they don't hit very low to the ground, and they are both very slow characters. Tug does have a very fast backthrow however, and I'm sure there will be tech down the line that is more than just spamming jump kicks that could throw this tier list into disarray. Spinal cannot hoist objects or enemies over their head, or grapple enemies at all. That might be the only good part about playing as a breakdancing shark: no accidental grapples that get you killed as a result.
Ba Ba is very fast, and can clear the entire screen with one jump kick. It also hits slightly behind him. He's just the best, despite his glass cannon status. L. Ektra has a front-flipping motion with her jump kick, so there's sort of multiple stages to it, making it very good, but weird to get used to. When doing a neutral jump kick (jumping straight up) with her, you want to activate the kick on the descent of the jump arc, as you can better hit stunned enemies that way.
Stun happens when the enemy keels over into a dazed animation, complete with the stars whirling above their head. They take more damage when in this state, and I think the game wants you to use the overhead/ground attack (Y, or Down+B) to hit them. But what you actually should do, is jump kick them. Bigger hitbox enemies will absorb several blows while in that state, so when you combine that with a jump kick that hits potentially 3 times, you get a lot of instakills (even on bosses). Sometimes popping a BLU Pill and spamming special may be preferred, depending on the enemy and character's special. Off the top of my head, Y.Y. & Leach (the giant grab bosses), and Chavez seem to stay stunned when spamming specials on them sometimes, allowing you to get many hits in. Take into account that your special will hit this stunned enemy 3 or more times per button press, and you might get like 9 hits in that are worth double damage before they wake up.
The Robot Arms are extremely strong. I know you're slow to move in them, but man it really doesn't matter when you one-shot everything, and three/four shot bosses with them. The Bumper Car is strong and fast, but you'll have to settle for Tok Tok most of the time, since the car appears in very few locations. Throwing objects are generally better than holding them as a weapon, and the Pipe/Wrench just suck because they don't do any more damage, but are very slow, and you can't throw them. There is a trick with big throwable objects, where you can kite them forward through the level without throwing them, and amass several in one location. This is useful if you know there's going to be a boss fight on that location. For example, the Tok Tok fight on the elevator on the Low-Levels path, already has a statue bust on the elevator. If you bring the safe from earlier in the screen to the elevator, you now have two big objects. If you wait until the boss spawns with his roller-skating friends, you can kill all of them by just throwing those two big objects (the bosses included).
Speaking of that elevator, there are a lot of pitfall locations in this game, like knocking enemies off the side of the many elevators throughout Paprium. You will lose a fat grip of life if you fall down these pits yourself, but keep them in mind when grouping enemies together. Either throw them off one by one, or hit them all in the general direction of a pit, and chances are they're going off the side and possibly dying immediately, or taking a buttload of damage before plopping back on the screen.
That's all I got for now. I think Very Hard will be the standard difficulty, since they don't scale like Streets of Rage. There will be more spawns, and you'll take more damage, but they won't have a bajillion health like Mania mode. Paprium difficulty is not that much different than Very Hard, in fact it may be faster than Very Hard because of the increase in AI aggression (better for enemy grouping since they run right up to you instead of linger on the edges of the screen).
Enjoy Paprium, tell a friend, lemme know if you have any suggestions to add to the leaderboard as I am open to dialogue. There's still a lot of secrets left to find, that could change how the categories are arranged and things of that nature. Later!