Here is the full list of all 51 Starbound achievements. It takes around 200 hours to unlock all of the achievements on Windows.
Recruit a penguin mercenary from the Beakeasy.
Complete the Cosmic Museum's cosmic collection.
Defeat the Ruin.
Return the Baron to the outpost.
Return Lana Blake to the outpost.
Destroy a robot chicken. Don't try to eat it.
Incapacitate an innocent bystander. You monster.
Become champion of the arena. Crush your foes like an orange sorbet.
Return Tonauac to the outpost.
Harvest 30 unique crops. Start thinking about who you'd like to romance and that barn extension.
Defeat the Shockhopper MK I. Notice it rarely hops.
Return Koichi to the outpost.
Kill 100 small flying monsters. They had it coming.
Return Nuru to the outpost.
Defeat the dastardly Dreadwing. Bring joy to penguins everywhere.
Capture your first bug with a bug net. Esther would be proud.
Recruit your first crew member. Captain!
Augment your EPP. Now it's an AEPP.
Obtain an entire set of armour. Now use dye to make your armour fabulous.
Fix your ship.
Find a Codex. On Earth it's rude to read other people's diaries.
Collect your first musical instrument! Keep playing, even when everyone begs you to stop.
Meet Esther.
Defeat Mother Poptop. Every Poptop you meet from here on out is a lonely orphan.
Practice your chef skills. Try not to harm anyone.
Harvest a crop. See what happens when you eat it.
Complete a quest! Joke's on you, there isn't any XP in this game.
Survive the Protectorate. It could have been worse.
Obtain the mythical perfectly generic item.
Complete Mazebound. You only need to beat it 300,000 times to win a slide whistle.
Attract your first colonist. Make sure you treat them right.
Restore a complete fossil. Make wild assumptions about what it used to be.
Capture a monster. How does it fit in that tiny ball?
Obtain a cool vehicle. Pop some sweet wheelies.
Recruit one crew member from every race. It's like a teeny tiny protectorate.
Complete 10 quests for your colonists. Feel like an asset to the community!
Complete 25 quests for your colonists. These guys sure do ask a lot of you don't they...
Complete 50 quests for your colonists. When did this become your full time job?
Obtain a complete alpaca costume. Use it only for good!
Build a large colony. Well done Protector!
Build 5 homes in a very small space. This isn't a healthy way for anyone to live.
Kill another player. Unity is overrated anyway.
Move a planet's worth of blocks. If you weren't using a Matter Manipulator you'd be ripped.
Catch 42 unique bugs. Give them all funny names.
Prepare at least 100 unique dishes. Bonus points if they're edible.
Unearth 55 unique fossils. Try not to pay attention to the ones that are alarmingly humanoid.
Collect at least 50 unique action figures. Insist to your friends they're actually called statuettes.
Collect 210 unique pieces of armour. See how many you can wear at the same time. (Spoiler, it's 3).
Find 100 unique codex items. Study them all, prepare for a pop quiz.
Recruit at least 12 crew members. Consider starting a pension plan.
Attract 10 unique tenants. Marvel at their collective peculiarity.