Wavebursts consist of bursts that make you slide on the ground and merge with the floor to gain speed. They were named after SSBM's infamous wavedashes.

In order to execute a waveburst you have to be running on a platform. Then you have to burst in front of your character (where it is running), below the platform. For example, if your character is running on a horizontal platform facing right, you have to click down right of it at a 30° angle.

You can click multiple times to gain more speed but it will also make the character merge deeper with the platform and it will be harder to jump from it.

Chain slinging is just slinging without any interruption. There is no cooldown, use it. You need lightning fast reflexes though.

Sling boosting is done by executing a burst just after slinging. It can be used in 2 cases: you want to gain speed, or you want to quickly change direction after slinging. It also serves the purpose of breaking walls while slinging.

This can of course be used with chain slinging. Some levels can be done with only one chain and you should burst everytime you sling to reach maximum speed on those levels.