Figured I'd post some time saves here and add to it if I find anything else.

Checkpoint Skip

You can jump over the checkpoint before the eye chase and save ~5 seconds after the intentional death.

I tried skipping the checkpoint before the first lava section as well, while you can go under it to avoid it triggering, it does not appear to have enough space to make it to the other side without dying or triggering it.

Egg Skip #1

This lets you skip the roundabout section after the Musk Rat fight to get the egg early, saving ~10-15 seconds depending on the amount of tries it takes and if you choose to use the safety save in the next room.

I think this is pixel perfect, it seems to be pretty consistent if you slide to the pixel shown below and then jump, immediately holding left.

Egg Skip #2

There are two ways to do this one, one from the left side and one from the right. The left side being a little harder, but saves ~5-6 seconds off the intended route. The right side saving ~3-4 seconds. The corner jump at the end is pretty tricky either way, as long as you can do it within ~3 tries you aren't losing any time.

Left Side:

Right Side: