Here is an overview of all TASes with humanly viable gameplay that have been made to show what's possible in this game.

A 131 Star "Low-Optimized Tool Assisted Demonstration" has been made by StarrlightSims and finishes the category in 1:13:55:

This is an update with all optimizations to this LOTAD, saving roughly 151 seconds altogether:

The 45 Star Power LOTAD made by FrostyZako in 41:51:

Note that this run loses 16 seconds in 4-4 and 12 seconds in 8-1. See the 131 Star LOTAD and the LOTAD Fix for more optimized gameplay in those levels.

This is an 8 Star Theory TAS which shows how to finish the game with only 8 stars. The gameplay in it is very bad but it is not meant to be flawless and optimized:

There is an old 131 Star Theory TAS that finishes in 1:35:08 but got beaten by Starrlight's LOTAD by over 20 minutes. A lot of the time was lost to unnecessarily bad gameplay and strategies whereas another part of the time was lost by having gameplay that is more realistic for real runs. Therefore it can be used as a reference for runs:

Soon after this Theory TAS was finished, World 8 was redone because a lot of time was lost there, and 4 minutes ended up being saved to the first run. The timesaves here almost all come from more senseful strategies, and as such it is definitely preferrable over the World 8 from the first Theory TAS: