A 2 vs 2 Fight, best of 5. You can fight against humans or AI, but your teammate will always be another human (barring connection mishaps).
Each player begins facing off against a single opponent- the two pairs of combatants on different parts of the battlefield. The first choice to make is whether to try to take out your opponent, or run to doubleteam your partner's opponent, then finish off your own. Both have their merits, but do consider your relative speeds- if you're a Shugoki facing off against a Peacekeeper, you're probably not going to outrun them.
The other factor, of course, is what the other pair is doing. If you do stand and fight, be aware the other enemy may be sprinting toward you even now, ready to attack from behind. Even worse, they may have already killed your teammate. You'll know this from onscreen messages and the little skulls in the top right corner of the screen.
But while there are little pointers to both enemies and your partner, there is no minimap in Brawl Mode. If there is a second living enemy still on the board, just keep a lively eye for sneak attacks, because you never know quite when they'll appear.
If you find yourself outnumbered, disengage and try to split them up, if possible. If one of them is noticeably faster than the other, try to hit-and-run them, while staying well out of the slower one's range. If you do end up doubleteamed in a corner, well, you'll probably die, but if you focus solely on blocking (and countering guardblocks), you might just build your Revenge meter fast enough for a fighting chance.