Neverwinter

NOTE: As far as I can tell, you should be able to get this achievement with a mixed class set of Huntsman's Gear. I already had the achievement so the xbox achievement didn't pop, but when I gave another toon a full set of Huntsman Gear not for it's class, then the in-game achievement triggered for collecting a full set of Huntsman Gear. The in-game collection did NOT trigger.

Huntsman's Gear is the second highest level of the 5 new levels of gear in Chult. It is item level 480.
Huntsman Gear binds on pickup to Account.
Note: You only need the Head, Chest, Arms, and Feet. The Rings aren't required for the achievement.

You can get Huntsman's Gear as drops from Bosses in the Tomb of the Nine Gods.
Also, Huntsman Gear is in BOTH final caches of the TONG! (Thanks FxH Final!)

The Huntsman's gear like the Pilgrim's gear has more Recovery for my GWF than the other sets offer, otherwise a decent mix of the usual good stats.

Huntsman's Gear has a mix of useful bonuses:
Helm: +1% Damage against Hunts in Chult.
Chest: When in combat with only one enemy, your Def is increased by 1000.
Arms: When in combat with only one enemy, your Power is increased by 1000.
Feet: When you kill an enemy, your Run Speed increases by 1% for 10 seconds. (max stack 5)

The 4 different Huntsman rings all are item level 480 also, double-slotted, but no double defense or offense slots. And no Crit/Power combo, just Crit/Arm Pen, Crit/Rec, Power/Rec, and HP/Defl.

Huntsman Assault Ring: Crit/Arm Pen: When in combat with only one enemy, your Arm Pen is increased by 1000.
Huntsman Raid Ring: Crit/Rec: When in combat with only one enemy, your Crit is increased by 1000.
Huntsman Restoration Ring: Power/Rec: When in combat with only one enemy, your Rec is increased by 1000.
Huntsman Ward Ring: HP/Defl: When in combat with only one enemy, your Defl is increased by 1000.