There are 11 exotic weapons and 4 armors per class added in the Forsaken DLC. You will have to have some luck to complete this achievement, but some are available through quests. I will start with the ones through RNG first.
Weapons:
Cerberus +1, Trinity Ghoul, Two-Tailed Fox, Black Talon, and Queenbreaker.
Titan Armor:
One-Eyed Mask, Ursa Furiosa, Heart of Inmost Light, and Antaeus Wards
Hunter Armor:
Shards of Galanor, Oathkeeper, Sixth Coyote, and Gwisin Vest
Warlock Armor:
Contraverse Hold, Chromatic Fire, Phoenix Protocol, and Geomag Stabilzers
There are also four available through quests, and two that only drop from specific things in the Forsaken DLC
Wish-Ender- Available through a quest that starts in the
Ace of Spades-Available through quest you receive at the end of the Forsaken campaign avenging
The Chaperone-A quest that begins at the end of the campaign given by Amanda Holiday
Malfeasance-From a quest that begins by killing a special boss in the new game mode, Gambit. This boss spawns very rarely but will have a higher chance at spawning on the 3rd and final week of the corruption cycle.
Lord of Wolves-Has a high chance of being dropped from the Wanted bounties from Spider on the Tangled Shore.
A Thousand Voices-Only available through the chest at the end of the Last Wish raid after killing
in the chest room. Only a chance of having it drop.
You only need 10 total, and they carry between characters. I got mine with 6 weapons, 3 Titan Armors, and 1 of the Hunter Armors. For the ones that drop by RNG I would recommend doing any bounties, or daily and weekly objectives that drop Powerful Engrams. If you have any questions feel free to leave a comment on this guide.