Before We Leave

You tame a Sphinx with a fully upgraded museum. After I had fully upgraded the museum, my peeps then successfully answered three questions. When they answered the third question, the achievement popped and a message appeared that the Sphinx was now an ally and would become a source of power for buildings on this island.

The Sphinx is a weapon that is built on top of a "mountain" (the structure you mine stone from with a quarry). You will be warned by a message in the game if a scout ship or colony ship discover one while traveling near an island. Once you colonize this island, you will be able to research the museum in the tech tree.

The Sphinx becomes active after an island is colonized. It will target a structure, ask a question symbolized by three shapes over whichever building it is targeting, and then fire upon that building, damaging it. You can repair the structure afterward. It will never target your port.

You need wood, tools, stone, and glass to build a museum.
First upgrade is 20 green research.
Second upgrade is 20 red research.
Third upgrade is 20 blue research.
Fourth and final upgrade is 20 purple research.

If you haven't found a planet with purple research, you can find purple research on your home planet by exploring ancient shipwrecks with a submarine. In order to build a submarine, you will need to research Advanced Shipping and then upgrade your Shipwright.

Additionally once you have a submarine, you can discover the Crystal Island on your home world by exploring a unique sunken ruin in the ocean that has purple crystals on it. The Crystal Island will appear allowing you to colonize it in order to reveal new technologies, yellow research, and the crystal resource. You must research Transmogrifier in order to unlock the ability to mine these crystals. Once you research the new tech, Research Institute, you can build this building which will gradually generate all 4 main research colors, starting with the one needed most, which should be purple.

I do know your peeps in the museum will correctly answer a question without a fully upgraded museum. I tested this on a second Sphinx in which the museum lacked the final purple research upgrade. BUT they only seem to answer questions and thus the Sphinx does not fire. It does not appear that the Sphinx will become tame until it recieves answers to its questions from a fully upgraded museum. I ran the game on the fastest setting for nearly an hour and my peeps answered around 15 or more questions correctly and the Sphinx is not yet tamed.

On some islands you can see a strange metal structur with a tilted head (base looks like a stone mountain).
On this island you have to build a museum (can be researched with yellow intel after finding the sphinx).
Be aware that you need intel of all colours to fully upgrade the museum - so store it already upfront to save time, otherwise the sphinx will destoy random buildings on the island. Each upgrade will increase the chance to tame the sphinx.
Feel free to add further informations about this achievement in the comments.