Here is the full list of all 38 Under The Waves achievements.
Unlock all achievements
Craft 25 oxygen sticks
Craft every upgrade
Find all collectibles
Find all crafting recipes
Craft every decoration
Unlock all stickers
Unlock 75 logbook entries
Play with the music box
Watch all optional TV programs
Upgrade Moon's engines to electric
Rescue a squid from a wreck
Have Stan sing a sea shanty aboard Moon
Find the galleon
Break Moon beyond repair
Find closure
Find solace
Complete Stan's seventeenth day underwater
Complete all photography missions
Pick up 10 empty oxygen sticks
Complete Stan's sixteenth day underwater
Complete all routine missions
Clean 50 oil traces
Pick up 50 pieces of plastic
Complete Stan's fifteenth day underwater
Reach a score of 2500 on the punching bag
Reach a score of 5000 on the guitar
Succumb to ?????
Complete Stan's fourteenth day underwater
Take a peek at the surface
Pick up 25 pieces of plastic
Use a repair kit on Moon
Complete Stan's third day underwater
Learn more about a blue whale
Complete Stan's second day underwater
Find a collectible in a wreck
Interact with the communication antenna
Complete Stan's first day underwater