Super Monkey Ball Banana Mania

For this achievement you'll have to clear Reverse Mode.

Reverse Mode consists of 10 stages, where you start at what is normally the stage endpoint.

First thing's first, you'll want to head to the point shop from the main menu and go down to the special category.

There you'll find the reverse mode available for purchase (iirc 10000 coins).

General Tip for any stage (this set or otherwise):
If you tilt your left thumbstick very slightly left or right it will turn the camera without causing movement, which can make lining up some more precise movements a good bit easier.

General Tips by Stage:
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1. Branch
Not much to this stage, just manage your speed on the first ramp so you don't overshoot and fall off.

2. Waver
Hold completely straight for the first and thinnest wave.
Back off the speed a bit on the second set so you don't overshoot the corner.
After that it only gets easier as the waves get thicker, just keep managing speed towards the end of each wave so you don't overshoot the flat areas.

3. Free Throw
This one can be tricky.
The ramp will launch every 5 seconds after the start (looks like X9.8-ish and X4.8ish on the clock) to me.
You want to time yourself to go forward along the ramp and have it launch as you get near the end of it (be going as straight as possible, any deviation left or right will likely launch you too far to the side).
From there it is likely a good helping of luck that you don't overshoot the platform. Use the minimap to help align yourself and see where you'll land.

4. Rings
Another one like Waver where it gets easier as you go.
Start by launching at the steepest angle you can left or right, and ride the lip to the opposite side of the ring.
Keep that strategy for each subsequent ring, although they get more forgiving as you go. Once you get to the final ring it is flat, so just keep your nerves about you and roll on in to finish

5. Amida Lot
Wait for the pegs to go ahead of you (should be less than a second) then go straight until you get to the closest crossing that goes to the right before the goal.
Cross to the right then back to the left into the goal. Be as quick as you can, the pegs will eventually come by and knock you off.

6. Carpet
This level consists of two ferris wheel type contraptions, for the first, wait until you are able to drop onto one of the platforms, then wait for it to reverse.
Once you near the top of the ferris wheel, drop onto the second platform of the ferris wheel.
Wait for the wheel to bring you back up then get onto the flat area.

For the second ferris wheel wait for it to turn where the platforms are closest to you. If you got to this point as fast as you can, you'll wait a full rotation.
From here you have two options:
1. Ride the platform you get on to the top and hop onto the end of the course. This is a bit risky but is much faster.
2. Drop onto the second platform of this ferris wheel and wait to be brought all the way around. This is safer, but is a good bit slower. I didn't personally do this method so I'm not 100% sure but I think you'll still have enough time.

7. Clover
No real gimmicks to speak of here, the path is a bendy clover.
Be sure you have enough speed for the curved parts to not slide off of the bottom of them, but not so fast you overshoot the flat parts of the path.

8. Punched See-Saws
For this level, just start on one side or the other of the first see-saw and alternate sides after/between each hole.
The only somewhat tricky part is you need it to lean to one side a bit by the end so you can dismount onto the flat platform after each see-saw.
Do that procedure twice (once for each see-saw) and this level will be behind you.

9. Checker
I had a ton of trouble with this one.
This requires a bit of a steady hand, as the entire level is made of squares about the radius of your ball, checkered with holes to fall through.
Best advice I can give is to rotate the camera so that going straight will have you moving on a diagonal, then carefully move forward in diagonal chunks.
As always be careful not to overshoot at the end of each forward jaunt.
With enough patience you can see this one through.

10. Polar Large
This level looks pretty daunting.
The idea is that you have to cross from biggest to smallest ring radius by moving from piece to piece inwards, but there is a trick.
The first ring from the one you start at rotates constantly. You can use this ring to launch yourself towards the goal and skip basically the entire stage.
My tip is to hold still and push the stick all the way forward at about 56.2 seconds on the clock.
From there a bit of left stick adjustment and luck is usually required, but that timing usually gets a consistent launch towards the center for me.

If you have trouble following this advice or have a special tip for a level that you'd like added, comment it and I'll update as needed.

Hope this helps!