There are 14 hats you can find in the game. 9 from the Return to Eden base version and 5 from the Seed of Evil DLC (although most lists of the hats online only give 4 for the DLC which is incorrect). The map areas are not very big so just look around the area I list for each hat you need to find. All the hats are near enemies, so as long as you kill the enemies in each area, you should also stumble across the hats.
Be warned that this achievement glitched for me at first. It did not pop until 2 days after I found all of the hats. The achievement tracker increments ~8% for each hat found which corresponds to finding 13 hats. Since there are 14 available in the game, I suspect that it counts only one of the two Explorer Helms that are available.
Return to Eden:
- Snazzy Visor (Ark Outskirts)
- Aristo Hat (The High Road)
- Explorer Helm (The Fallen Angel): there are two copies of this helmet in the game
- Fertility Crown (Cave of Fear)
- Helm of Wisdom (The Iron Serpent)
- Borg Band (The Lair of Horned Devil)
- Grenadier's Delight (Spear of Heaven)
- Gladiator Helm (The Unenlightened)
- Explorer Helm (The Unenlightened): there are two copies of this helmet in the game
Seed of Evil:
- Grogg Helm (Mausoleum of Suburbia)
- Herpes Mask (Hall of Electric Coffins)
- Blue Oyster Cap (The Under-Ark)
- Polis Taco (Valley of Steel)
- Helm of the Speaker (Spear of Heaven): this is found during one of Pripp's side missions