Outcast - Second Contact

(The other solution is partially right, but missing some details, so I will attempt to be as complete as I can)

You get this quest from Zernar, the leader of Cyana (in Okasankaar -- the swamp area). He will tell you that the lighthouse's light is broken, and you need to fix it to get this achievement. There are quite a few steps to this:

- Climb the lighthouse and remove the old crystal. The lighthouse is nearby Zernar, you really can't miss it. Just do some clunky platforming up to the top and grab the helidium crystal.

- You need a new crystal, and you get it in Motazaar -- the lava/volcano mining area, which you can get to via the eastern portal in Talanzaar (the desert market area).

- First, find Ashkar, the town leader. He wanders a bit, but I usually found him in the middle of the map by the water salesman and the blacksmith. Talk to him and ask about the pure helidium for the boat light, and he'll tell you to talk to the miners. (I did not need the region's Mon for Ashkar to have the dialogue option)

- Go to the northwest in Motazaar and you will find these miners, one of whom is standing by an injured guy. Talk to him, and he will ask you to find some plants to heal his friend, which you can find in several places in the region (they look like prickly pear cactus), I believe there are some by the bridge you need to destroy for another achievement (the skinny path at the north most part of the map).

- Gather two of the plant and give them to the miner, and he will heal his buddy. After the animation, you can ask him about the big helidium crystal, and he will talk about a rock they found that needs to be extracted and crushed.

- He will (eventually) take the rock to the rock crusher just to the south of where you first meet him (looks like a big hammer, you'll know it when you see it). He really takes his time with this part, so maybe go do some other stuff while you wait. Eventually, return to the crusher and pick up the new crystal.

- You now need to find Azirad in the market of Talanzaar, who is on the southwest side, basically due west of the bottom of the big rectangle in the middle of the map. He will (slowly) carve the helidium into the shape you need.

- Once he finishes, take the crystal, return to the lighthouse, platform once again and put it into the slot. The light will come on, you'll get a janky cutscene, and the achievement will pop.

U need to have the Mon from motazarr for the dialogue option to open with ashkar.

Travel to okasankar from shamazar, speak to leader in the nearby village by the docks where the sankar fisherman are, talk about the broken light.

Travel motazarr and head to northen mine, speak to zile and ask for helidium, Hel go to rock crushing machine to get the stone. Collect and take to okriana to speak to the helidium carver, Hel carve the stone into the correct shape. Return to okasankor and climb the light tower near the docks, replace the helidium and voila! Achievement.