This achievement is for finishing the Illithid Enclave quest. The quest line that leads up to this quest starts with General Knox, as all these story quests do, and takes you to the Whispering Caverns. The enemies here are level 58+.
I think these are the quests you need to do, it's hard to tell since the game gives no indication of what are story quests and which are side quests, that I can see.
Into the Underdark (this is the one Knox gives you)
Dark Hunters
Prisoners of the Drow
Xorlarrin Outpost
Delving Deeper
The Payoff
The Overseers
Wrathforge
The Upper Vault
Thrall Keepers
Resonance Stones
Into The Unknown
Brain Damage
Unwilling Hosts
The Birthing Pools
Illithid Enclave
Note : Quest names were taken from the Neverwinter Wiki :
http://neverwinter.gamepedia.com/List_of_quests?cookieSetup=...