Any4-3

This is the main horizontal Checkers level in the run. Be careful to learn the exact jump timings as mistakes can be very punishing in this stage.

Optimal

Pay attention to the positioning of each dropdash. With correct positioning, you can usually reach your destination by simply maxing out your jump, releasing jump near the end if necessary, making the stage more consistent.
For the piggyback throw at 0:08.5, position yourself at the same height as the top coin and approximately above (slightly to the left of) the frog platform. Position the subsequent dropdash at the same height as the bee.
Aim to land on the left side of the platform at 0:13.5. Ideally you want to jump over both Taptaps and the fire gator without rolling through them and without dropdashing. If you roll through a Taptap you will lose maximum speed and need to dropdash again (ideally over the fish) to regain it. It's also possible to jump over the fish without dropdashing, but it's very precise and difficult to position.
The two dropdashes after the checkpoint are not max height and must be adjusted manually. Try to land as close as possible to the last bee, then buffer a max height jump.
Try to land directly under the bee after the buddy bubble at 0:22.5. The jump and bounce off the frog is consistent with a max height jump as long as the jump is positioned correctly.
After the frog bounce, the dropdash at 0:24.2 to the Cawbie is max height. Continue holding jump to bounce off it at max height.
After falling between the 4 Cawbies at 0:26, initiate the next dropdash after passing the horizontal position of the last one. This causes the frog to spawn in and jump out of your way. If you dropdash too early the frog will not jump and you will need to adjust to its position.
After bouncing off the frog, position the dropdash at 0:29 approximately above the left edge of the platform. You may need to briefly release jump in order to land on the snake. The bounce chain off the 3 snakes is max height. You may need to again release jump to land on the frog at the end. If you miss the frog bounce you can just dropdash.
After the frog bounce, release jump to land towards the left side of the rope. The rope jump sequence is: small, big, small, big, big. With correct alignment you will make it to the lower platform before the goal, but if you are too high or low you can dropdash, going over or under the snake as needed.

If all goes according to plan, aim for a 38 on this stage. If anything goes wrong, see the backups below.

Backups

This video demonstrates two backups to taking damage at common spots in the stage.

If you lose Checkers before the checkpoint, grab it, exit the level and go back to Magmaw Well for a buddy bubble. This is faster than continuing through the slow rope climbing with solo Marbles.
After taking damage on the third bee, hold jump to clear the pole with the damage-boost jump. If you maintain speed, you can grab the bubble and pass through the next bee with invincibility frames (I-frames).
After stomping the frog and swapping, piggyback, do a full-height jump and a full-height dropdash to reach the Cawbie.
If you take damage before the Snake chain, Marbles can go under the snakes by spin-dashing from the edge of the platform and gliding to the last pole. Make sure to go quickly or the rising lava column will block your path.
After recovering Checkers you can resume the normal route by dropdashing right up to the two bees, but if you get thrown off you can simply clear the final section with a quad jump or two.