Easy:
* Crush - Kill an enemy by crushing them with an object.
* Sticky Bomb - Kill an enemy by fixing a sticky shock grenade to them.
* Highfall - Kill an enemy by making them fall from a high place, usually over a ledge.
* Enviro Take Down - Kill an enemy with environmental explosion.
* Melee Finisher - Kill an enemy with the last hit of 5 hit melee combo.
Tricky:
* Air Strike - Kill an enemy with the Lightning Bolt move while Cole is in the air.
* Blast & Bolt - Kill an airborne enemy with the standard Lightning Bolt weapon.
* Flying Head Shot - Aim carefully, and take out an airborne enemy with a headshot.
* Flying Melee - Kill an airborne enemy with a melee attack.
* Unquenchable Thirst - Be like Tony Hawk and transfer to 4 different grinds without touching anything else.
* Premature Detonation - Kill an enemy by making a bomb-equipped kamikaze enemy explode near them.
Tough:
* Right Back At Ya - Use the Shockwave move to make enemy kill themselves with a grenade or rocket.
* Air Sticky Bomb - Like #3, but kill an airborne enemy by sticking a grenade to them.
* Insult To Injury - Stick a grenade to an enemy, but then kill them with another weapon (or melee) before it explodes.
* Whack A Mole - Kill a Conduit with the Thunder Drop move.
* Suspended Sentence - Kill an airborne enemy with the Thunderstorm move.
* Up Close And Personal - Kill 3 Enemies back to back with just the melee. Dont fire in-between.
Daft:
* Crowd Control - Kill 5 Enemies at once, easier with a grenade.
* Splash And Crash - While in the air, Shock an enemy and then hit the same enemy with the Thunder Drop move.
* Have A Nice Fall - Kill 3 enemies at once by making them fall from a high place. Again, easier with a grenade.
* Ride The Lightning - Kill an enemy with Precision while rail grinding.

Stolen from
here.