All 11 executions???????

1. Boomsheild - tap Y when carrying the Boomshield
2. Neck Snap - Pick up downed opponent and press X
3. Torque Bow - Press Y with Torque equipped
4. Sniper Hammer - Press Y with sniper equipped
5. Curb Stomp - Press X
6. Beatdown - Press Y when carrying a default weapon or anything without a special animation
7. Golf Club - Tap B standing still with Shotgun equipped.
8. Boltok (Magnum) Whip - Press Y with the Boltok equipped

And now the boring stuff but I guarantee these work and will get you the achievement

9. Melee with Torque - Just press B with torque equipped standing still
10. Melee with Sniper - Just press B with sniper equipped standing still
11. Melee with Gorgon Pistol (Burt Shot Pistol) - Just press B with gorgon pistol equipped standing still

Or instead of the melee with the Gorgon Pistol, just press B (don't hold it!) with the lancer.