Here is the full list of all 36 Super Monkey Ball: Banana Blitz HD achievements.
Clear a stage as Sonic the Hedgehog
Clear World 8
Clear World 7
Clear World 6
Clear World 5
Clear World 4
Obtain 4 Champion Medals
Clear World 3
Clear World 2
Clear World 1
Unlock all achievements
Clear World 9
Clear World 10
Obtain 8 Champion Medals
Obtain 9 Champion Medals
Obtain 10 Champion Medals
Clear the Casual Course in Time Attack Mode
Clear the Standard Course in Time Attack Mode
Clear the Expert Course in Time Attack Mode
Clear Time Attack Mode 36 times
Clear the Decathlon
Clear the Decathlon 36 times
Clear the Hurdle Race in 00:20.00 or less (single-player only)
Clear the Normal Course of Monkey Snowboard in 01:40.00 or less (single-player only)
Throw over 110m in the Hammer Throw party game (single-player only)
Obtain over 2500 points in the Monkey Target party game (single-player only)
Obtain over 2500 points in the Slingshot party game (single-player only)
Obtain over 5000 points in the Space Monkey Attack party game (single-player only)
Clear the Normal Course of Hovercraft Race in 01:30.00 or less (single-player only)
Obtain over 8000 points in Seesaw Ball's Normal Course (single-player only)
Clear the Normal Course of Dangerous Route with 02:00.00 or more remaining (single-player only)
Obtain over 3000 points in the Whack-a-Mole party game (single-player only)
Change the costumes of all characters except Sonic and clear a stage with each of them
Clear 100 stages in the Main Game using the same character
Collect a combined total of 3600 bananas through the Main Game and Time Attack Mode
Obtain secret bananas from any stage