Bullseye is unfortunately one of the weakest 2 star characters. Although his passive is decent, his single other move is weak in all but the rarest of circumstances.
Purple - Adamantium Bones: Bullseye's purple power is a passive, Adamantium Bones. This creates a Protect tile on a purple match by either team. These can eventually slow the enemy down. Since either team's match creates one, it often isn't long before the board is getting crowded. Also, anytime your opponent matches one to destroy it, another is formed in its place. At the same time, moves like Daredevil's purple are perfectly suited counters, creating the tiles and then immediately using that purple AP to destroy them.
Black - Murderous Aim: Murderous Aim has the potential to be the strongest move in the game. Except that it can never, ever be so. Murderous Aim creates 2 critical tiles at max level. If after those are created there are a total of 4 critical tiles on the board, he deals an additional 8,200 damage at max level. 8200 damage kills pretty much every single 2 star character, and a fair number of 3 star characters, in one shot. The additional damage done by four critical tiles should just about wipe the rest of the team, plus the resulting AP would charge almost all of your moves. However, the chances of this occurring are so low as to be impossible. Even if you were to save for two uses (which is a solid 32 black AP, by the way), finding places on the board to set a critical without it matching are tough. The only benefit to this move is that the player selects the critical tiles location, and while it can't directly target a special tile, it can be used to match with them.
PVP Summary: Adamantium Bones actually works pretty well against most teams, but his overall weaknesses don't make up for it.
PVE Summary: You can use Murderous Aim to try to remove countdown tiles, but that is about it. His purple move is pretty useless against computer teams.
Team UP: Murderous Aim actually is a nice team up to select. It allows you one get out of trouble card by easily matching with a stubborn countdown or special tile, and can provide the critical hit you need to get you over a hump. Also, since it is just creating a critical tile, you can use it at any level with equal effect.
Match Ups: Falcon immediately springs to mind, powering up some of the protect tiles could really mess up an enemy team. Bullseye also provides a good way to unload your black AP, which few other characters do.
Counters: No one particular, maybe someone who wants purple AP as to charge they will have to put up your protect tiles.
