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There is only one mode; online free for all, labelled FFA Tournament. When you select a character (out of 6; Sly Cooper, Parappa, Kratos, Radec, Fat Princess and Sweet Tooth) you automatically jump into a game with other people. I played yesterday evening and the match making was good for the most part; I got to jump into a game only seconds after choosing a character, which shows that the netcode is doing a fine job getting me with other people. It does a great job of registering everyone's movements, and I had absolute zero lag at all.
I only played 5 games before the beta inexplicably froze on me so I'll just tell you what I know. Because there is no training mode, i'll just tell you guys what's up with the controls and how you do crap.
I touched only two characters unfortunately; Radec (Killzone) and Parappa (you know where this guy is from lol), my personal preference characters seeing as how I love both franchises. Hopefully this is going to be a good coverage of controls seeing as how Radec is pure zoner character and Parappa is more of an in-your-face-guy.
There are three attack buttons, aptly labelled 'Attack 1', 'Attack 2', and 'Attack 3'. 1 is basically the short range combo, 2 is a long range attack and 3 is... I guess you could label it a special attack? Sort of like in Brawl (which this game doesn't really resemble much at all apart from
some minor things lol). Holding a direction or letting go and remaining in a neutral position when you press any of the 3 attack buttons gives you an different attack, and you'll also get a different variation in the air. If my calculations are correct, every character has about 24 attacks. There are no back-facing air variants like in Brawl. Sorry if the comparison to Brawl irks you but it's just the closest thing that resembles this at the moment lol. The attacks are up/down/left or right/neutral. Holding any of those directions when you do an attack will put out a different attack.
The entire game is centered around building meter. Normal attacks won't do damage at all and the only way to die/get score is hit by a meter attack. Meter attacks are done by tapping R2. They come in 3 levels. Level 3 meters (the cinematic attacks you see in the trailers) aren't really all that worth it seeing as how you can get just as much kills with a level 1 or 2 if you have enough finesse with it. Level 3s are basically screen clearers, and from my knowledge no one will spawn until the animation is over.
Of course, there's the block button. Holding it when you're grounded will let you block and pressing a direction while doing so will make you dodge in that direction and tapping it when you're in air will make you do an air dodge, much in the vain of Smash. I
think that you can get your guard broken but I've never managed to see it happen to anyone or myself seeing as how much more offense based the game is.
Then there's the obligatory taunt button, and grabs. Grabs are done with the right analog stick, which is pretty weird if you ask me; I've never actually gotten to do one. I think the direction you flick it is the direction you throw. I can't really see much use out of it unless you're a zoner heavy character like Radec, but his attack 1 forward is a much better spacing tool.
Lastly there's the pick-up-item-button which is what it says on the tin lol, from what I've seen there are only 3 items implemented; a rocket launcher, a speed boost and an exploding spike ball of some sort. Items are thrown or used with the attack buttons after you pick them up. You can't block with them equipped (unless it's the speed boost).
Only two stages are implemented; God of War's Hades (with a bunch of PataPon in the background... Derp.) and Ratchet and Clank's Metropolis. Both these stages got me real nostalgic and were just overall fun to play on. There are a few stage hazards every now and then like ascending/descending platforms, exploding walls, a rain of PataPon spears etc. It's really hectic and fun, and nice to look at too

So yeah, that's all. Tl;dr, the beta is hella fun and I can't wait until full release.