You will need Warp Drive for this, or have gotten very lucky/done some research on a seed specially for this. Once you have a small pile of Space Warper and enough fuel for Icarus for lots of FTL travel, get exploring your star cluster!
Check each solar system you visit for a planet with the rare attribute "Tidal Locking Perpetual Day and Night". This appears in orange text, so a quick scan over each planet should be enough. Once you have found one, just land Icarus on it and pop this achievement. This will also help with progress towards your achievement for visting at least 32 different solar systems, as this is quite a rare property in my experience.
NOTE:
You should either remember or mark this planet in the map for later. Unless you are doing this with an Artificial Star and Antimatter Fuel Rods with you, you'll need to come back here as part of "Let there be light!" to run an Artificial Star on the night side of the planet.