Abilities are the attacks you will map to your UI, and are used by holding and selecting one of the face buttons. Traps count toward this achievement; however, sustained skills (such as Envenomed Edge or Blade Honing from the Finesse tree) and buffs (such as Relentless Assault from the Might tree) do not! It has to be classed as an "active" skill, as well as being the skill itself that kills the enemy.
If you don't use too many abilities, simply return to the starting area toward the end of the game and one-shot a bunch of low-level enemies with Storm Bolt from the Sorcery tree. You can also do the Arena in the House of Valor (DLC) for quick kills.