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