Here is the full list of all 18 Spin & Roll achievements.
Complete any stage
Lose a ball to the void
Collect all of the purple coins in any stage
Collect all of the green coins in any stage
Complete any stage in under 25 seconds
Obtain your first platinum trophy
Successfully complete at least 5 stages with a platinum trophy
Successfully complete at least 10 stages with a platinum trophy
Beat all Classic mode stages with platinum trophies
Complete any Master mode stage with all gold coins
Complete at least 5 Master mode stages with all gold coins
Complete at least 10 Master mode stages with all gold coins
Beat every single Master mode stage with all gold coins
Lose a ball to the terror of the slimes!
Lose a ball from an obelisk bolt
Lose a ball to a dangerous red bomb!
Lose a ball to a spikey
Lose a ball to a spike-plate