For this achievement you need to change at least one of your warrior classes to a berserker, one of your cleric classes to an engineer and one of your mage classes to a zephyr then play in a quick match or co-op game with all three of the classes. You do NOT need to use all three in one match, it can be split up. Although it's not too difficult to use all if you die at least twice.
But before you can play as the new classes you have to unlock them in one of two ways:
1) Do three special quests for them which I'll detail below
2) Unlock them with 20 happy tickets.
To unlock the Berserker class you need to complete quests #33, #36 and #44
#33 - "The Champion" - The most kills in a single game
#36 - "Kill 'em all!" - Kill all enemies in 1 game
#44 - "The Master Swordsman" - 100 total kills as any warrior type
(or you can buy him for 20 happy tickets)
To unlock the Engineer class you need to complete quests #23, #53 and #54
#23 - "The Finisher" - Destroy Big Tower 10 times
#53 - "Special Forces" - Destroy Big Tower without losing any HP
#54 - "Omaha Beach" - 300 kills using the ballista
(or buy it with 20 happy tickets)
To unlock the Zephyr class you need to complete quests #15, #43 and #52
#15 - "Dreaded Mage" - 30 total kills as any mage type
#43 - "And Becomes Legend..." - Appear on Hero Pop-up 50 times total
#52 - "The Twilight of Magic" - Kill 500 Mage types
(Or use 20 happy tickets)
After they're all unlocked just play a game and use them at least once and the achievement is yours!