Here is the full list of all 45 Broken Age achievements. It takes around 12-15 hours to unlock all of the achievements on Windows.
Get to know a stranger
Execute a PERFECT escape
Endure a tight situation as long as you can
Complete all rescue missions with zero errors
Take Control of the Boom Arms
Inhibit a powerful entitiy
Travel to a forbidden location
Disrupt Shay's daily routine
Make a Spoon Sweat
Examine all breakfast options
Feed two different people a healthy snack
Leave an isolated town
Reunite a mother and child
Get to know someone in a precarious position
Escape the Maidens Feast
Learn all you can about Sugar Bunting
Complete Broken Age
Stand up for someone even though you haven't met her
Complete Act 2 of Broken Age
Chart a course away from danger
Find a genius
Return a missing spaceship part
Commission a custom garment
Get a family member's help on a big project
Return a heavy duty spaceship part
Clear up a tangled situation in one attempt
Reconnect with some old friends
Uncover an unsavory scheme
Deploy a weapon of mass destruction
Remove 8 sad faces from the Bassinostra
Get to the ship's brain
Answer some tough questions quickly
Complete Act 1 of Broken Age
Take down Mog Chothra
Unlock all Broken Age Achievements
Hear 20 reasons why Gary won't grab that
Find 30 unique reactions to the Spoon
Visit someone in jail
Tell a great joke in one attempt
Follow up on a successful performance
Talk to the boss
Make someone strut their stuff
Stand up for someone even though you haven't met him
Start a group dance party
Complete Broken Age in under an hour, not counting loading and paused gameplay.