Here is the full list of all 28 Lovers in a Dangerous Spacetime achievements.
Defeat King Cepheus.
Have 20 cells at one time on the Metal-Beam shield.
Escape a white dwarf without shooting or ramming it.
Defeat Orion.
Deliver the final blow to Orion using a solar flare.
Defeat Cetus.
Fill up all gem slots in a fully upgraded ship.
Pirouette 15 times in a single level.
Finish a level without crossing paths with your partner.
Defeat Ursa Major.
Throw a gem into a station that is being used by another player.
Beat any level in two player mode.
Finish the tutorial.
Use every station in a single level.
Beat any level with the help of your trusty space-pet.
Finish a level after removing all fog of war.
Finish a level without taking damage.
Play through a campaign without using any gems.
Earn one of each type of ship badge.
Rescue every captured friend.
Defeat Ursa Major without taking a punch.
Defeat Cetus while its head is underwater.
Remove all of King Cepheus's shields.
Have 10 unused gems in your ship at one time.
Use three different types of Yamato weapons in a boss fight.
Survive after being fully enveloped by a bomb trap.
Kill 20 enemies with security guns in a single level.
Make two Power-Metal missiles collide.