To unlock the achievement you need to obtain every item listed on your invertory. They are the following ones:
N31L's head can be found near the Polar Peak's gate. After putting it, you need to do some challenges for him before gathering the rest of the itens.
See N31L's page for details.
You need all of the elemental cores and the X-Quisite core.
Weapons of Rock
You need the four Wonder Weapons to be built for this one. All of the four crystals are unlocked by the same way, see Arcane Core and X-Quisite for details. After obtaining the 3 parts for the weapons, they should be assembled at their respective places, an alien card that can be found on each section of the map, each one with their weapon's name written.
Face Melter: You will find the card alien in the Journey into Space. You will need the Rocket Toy that should be obtainable after putting 3 Blue Tokens at the Souvenir Machine to your right. For the Battery, you need to turn on the portal and throw a Frag Grenade inside. The grenade will come out of the portal and you need to carry this grenade to the Pack-A-Punch portal, throwing the grenade inside the portal will drop the Battery. The crystal for the Face Melter is the blue one, so you need the Electric Elemental Core.
Head Cutter: You need the Yeti Toy that should will drop from the Souvenir Machine at the Polar Peaks after putting 3 Green Tokens inside. For the Battery, you need to buy the Cryo Grenade and throw it at the Yeti's mouth near the Polar Peaks entrance. The Yeti will spill a chilling breath that will freeze the zombies and you need to kill 10 frozen zombies with a headshot, after hearing a screech, the Battery can be found by the Yeti's hand near the portal. You need the yellow crystal, so, the Wind Element Core.
Dischord: The alien card is found inside the Astrocade. You need the Disco Toy that can be obtainable by putting one of each token inside the Souvenir Machine near the Astrocade entrance (the door near Blue Bolts). The Battery can be obtainable by shooting targets scattered around the map that can only be seen while using the glasses droped by Zombies, after shooting 5 targets, the Battery will appear inside the Astrocade. You need the green crystal, so the Poison Element Core.
Shredder: The alien card is found on the Underground section. You need the Alien Toy that can be obtainable by putting 3 Red Tokens on the Souvenir Machine in Kepler. The Battery can be found on the back of the boat that comes from time to time near the Bang Bangs, wait for the boat to come and you can see the Battery, just shoot it and it will appear at the colored fountain. You need the red crystal, so, the Fire Element Crystal.
See Sooooul Key (Achievement) for details. You do not need to complete the Main quest.