Here is the full list of all 12 Staying Together achievements.
Jump 30 times in a single level
Complete a level without collecting any heart pieces
Retry a level 10 times in a row
Stay airborne for 3 and a half seconds
Collect all heart pieces on all levels
Die with both characters at the same time
Complete the first 10 levels
Die while frozen in ice
Complete a world in hardcore mode
Complete all worlds in hardcore mode
Complete a time attack level with exactly zero time remaining
Pass all levels in time challenge mode