This achievement requires you to kill 5 enemies with 5 different heavy weapons, there is a total of 8 heavy weapons, 3 of which are DLC. You should already have one heavy weapon kill before you meet the illusive man, this is because before you go down the elevator Miranda tells you to use the M-100 Grenade Launcher to destroy the mech's that are coming through the door.
A second easy heavy weapon kill is the M-451 Firestorm, you can acquire this weapon through natural progress of the Zaeed loyalty mission.
A third easy heavy weapon kill is using the arc projector if the arc projector dlc has been downloaded, This weapon will be unlocked as soon as Shepard acquires the Normandy SR2
A fourth heavy weapon kill could be using the ML-77 Missile Launcher, this weapon can be acquired from the Normandy research station after one heavy weapon ammo upgrade have been researched, The ML-77 Missle Launcher requires 5,000 iridium.
A fifth heavy weapon kill could be using the M-622 Avalanche, this weapon can be acquired from the Normandy research station after two heavy weapon ammo upgrades have been researched, The M-622 Avalanche requires 15,000 iridium.
A sixth heavy weapon kill could be using the M-920 Cain, this weapon can be acquired from the Normandy research station after three heavy weapon ammo upgrades have been researched, The M-920 Cain requires 25,000 iridium.
A seventh Heavy weapon kill could be using the collectors particle beam, this weapon can be acquired during natural progression on Horizon
The last heavy weapon kill could be using the M-490 Blackstorm Projector, this is a preorder dlc weapon which cant be acquired any other way, If the player has the weapon it will be available once Shepard acquires the Normandy SR2.