Here is the full list of all 13 Dolphin Up achievements.
Get to Mars
Do a Starslide
Score 1,000,000 points
Score 100,000 points
Score 100,000,000 points
Attract a school of 10 fish
Do a Frontside Rewind and a Backside Rewind in the same combo
Hit four rings and get to Saturn in one game
Do a Triple Carnival
Stay in space for 20 seconds
Do a tailslide for at least 10 seconds
Get to the restaurant at the end of the universe
Keep a game going for 2 minutes and 30 seconds