You've three forms of attack. Melee ("X"), magic spell ("B") and range ("Y"). You won't get all the attacks at once. Instead, they'll unlock one after another, with some transition period in between for you to get familiarized with the attack.
You'll unlock the "fire" magic spell first, followed by melee weapons next, and ranged weapons a while later. For the melee and ranged weapons, you'd need to press "Start" to go to the Armory in the Sanctuary to choose your weapons of choice.
After which, all you need to do for this achievement is to use all three types of attack once on enemies. These can be done on different enemies, at any time, and in any order.