Magic is invoked by pressing LB and a face button.
In the order earned
LB and Y - fire (fireballs drop)
LB and B - earth (earth shakes and rocks grow upwards)
LB and X - water (freezes enemies in an ice storm)
LB and A - air (unleashes a hurricane and lightning)
You will be told when new magic is unlocked, and when you can press Back to upgrade (spending the XP you have earned).
Simply kill an enemy with each magic to earn the achievement.
The water/ice magic can be useful on larger enemies, allowing you to cause additional damage while the enemies are frozen.