You must fully upgrade any skill from any of these categories: Biotics, Melee, and Abilities
I found most skills/ abilities in this game worthless, best skill is Pull, once leveled up it will let you Pull up to three weaker enemies in one shot.
As for going for this as quickly as possible, upgrading a Melee or Ability will cost a little bit less than fully upgrading a biotic.
If you are going for this achievement:
You will obviously get this one along the way