After completing Expert and Expert Extra without continuing, the Master floors are unlocked. Note that, unlike the sequel, the Master floors are NOT their own difficulty and can NOT be directly accessed from the difficulty select! Because of that, it is strongly recommended that you get infinite continues before tackling such a tall order, as you'll most likely burn through about 30 of them before beating them all.
Master 1 (Wave Master)
For the most part, just hold up, but be sure to control your speed in case you ged ahead of the flow of the platforms.
Master 2 (Fan Master)
Perhaps the easiest Master floor, you simply have to roll down each fan, being sure to stop on the white parts to avoid being knocked off.
Master 3 (Stamina Master)
Stamina Master starts with a variant of the 0.5-width peak in Expert 7 (Exam-C), but it's longer and only 0.1-width. After slowing down to avoid hitting the pole (which will cause an inevitable fallout if you do), you can either take a leap of faith and try to drop down onto the goal, or instead try to navigate the moving platforms and roll down the vine to go in the Goal normally.
Master 4 (Spring Master)
There are two ways to do this level: either roll down the carpet and stop at each white square, or intentionally let yourself get hit by the short wall in front of the carpet and try to land on it, giving a huge distance boost and possibly letting you get to the goal in one shot.
Master 5 (Dance Master)
A distant cousin of Blocks (Beginner 8), Blocks Slim (Advanced 9), and Dodecagon (Expert 6), Dance Master has the square in the middle break apart... and cover up the floor upon which you are. Try to avoid the squares and go around to the Goal, or get pinched by them and ride on top to the Goal.
Master 6 (Roll Master)
Either follow the red marks in the dodecahedron, or roll southwest (assuming you start facing north) and drop right in.
Master 7 (Edge Master)
If you've played Master Extra 10 in Super Monkey Ball 2, this shouldn't be too unfamiliar to you, just note which way the arrows on the pole point and roll in the opposite direction, going directly against the spin of the platform.
Master 8 (Dodge Master)
Simply avoid the pegs (which all go in circles) and go straight to the Goal.
Master 9 (Bridge Master)
This is close to Stamina Master in terms of how much rage it has induced, but is a bit easier because the really narrow parts can be jumped over by rolling off the twelfth segment, bouncing off the edge of the thirteenth, and landing right in the Goal.
Master 10 (Monkey Master)
Just watch AiAi's movements and curve your trajectory to line up with the Goal.