I love to play as Kat, I she became my main when released (been taking a break trying to get 300 w/ all). Although you don't see many Emmetts using it, his shotgun is his best IMHO.
Few easy guarantees (that you may or may not already know)
Level 1 (w/ Shotgun) - Side square then R2 immediately
Level 2 - Get your opponent to approach you in a corner then call down your Level 2, unless they have great reflexes or it glitches they're dead. Upgrab works too (unsure if 100% or just increased chance)
Level 3 (Stage Clear, sort of) - Just immediately hit (O) >> Strafing run is very quick and there are tracing missiles that will go after the opponents.
Level 3 (Control) - Always hit (Triangle) to deploy your air mines. Jump plenty and mash (Square), b/c when coming down from a jump you crouch some and can shoot a bit lower. And (Air Down Square) to stomp with a wider radius.