Pow, Right in the Kisser!:
Performed 50 Crippling Strikes

Who’s the Bully Now?:
101 advanced enemies defeated

Both of these achievements can easily be obtained during the challenge mission: Ballroom Blitz.  It’s easiest to go for these at the same time.  Load up the mission, then hop onto the turret directly in front of you, and unload on the continually respawning enemies.  The larger guys will count as “advanced enemies.”  When the special bar fills, hop off the turret, and perform crippling strikes (RB+X) until it has drained.  Then, hop back on the turret and repeat until the achievements unlock.  Good luck!