This is a missable story-related achievement that can only be earned while playing the Gaea campaign. For this achievement you must find the three pieces of research for the Green Laser (aka Walrus Laser MK. II). Much of the information on locations came from this thread on developer's forum. On the islands in the campaign accessible after Outpost but before Fulcrum there is a beaten up brown/rust-colored structure with a radar dish on the roof and a red panel next to the door. Approach those in a Walrus and press when the hand icon appears. You will be told a small amount of detail on what you found.
There are three pieces of research required, one found on each of the three different island climates. You only need visit the structure on one of each climate. The buildings exist on the other islands, but do nothing when you interact with them. When you find one on an island, you get a completed task on the island overview of Laser Prototype: Test Log - [Climate] where "climate" is replaced with the climate type of the island.
Beacon: On the northwest side of the island there are two hills out in the sea, with only a small isthmus of land leading to them. The building is between the two hills.
Evergreen: On the east side of the island is a lake with a tall tower next to it. Just to the north of the lake in trees is the structure.
Bacchus: On the southeast corner of the island, easily visible from air or land if you start at the lake and move south.
Endymion: On the northern end of the island, roughly halfway between a Walrus garage to the west and a small base with a repair and ammo dump to the east. Very easy to spot from the air, quite difficult to see from the ground.
Taksaven: In the compound with the command center is a power station. Due west of that, on the shore side of the mountain, tucked into a little clearing. Very difficult to see even from the air unless you have the sun setting. Getting there really needs the manta hook, which you don't have unlocked yet when you capture this island.
Granite: On the northern part of the island there is a circular crater/lake. Directly south of it are two turrets at a road intersection. The building is between the lake and the turrets, and slightly to the west.
Vattland: On the northeastern island, all the way at the southeastern corner. You can actually see it from the carrier when you first arrive at the island, up on the side of a hill facing east.
Isolus:There is a small lake right in the middle of the island, and the structure is just to the south of that lake on the southwest side of a hill.
Lingard: On the east side of the island, just to the southwest of the ammo dump tucked up against the hill.