Level 1 Guide

In my mind, this is a 4 part level
Part 1: The area before the wave of enemies. The only thing you need to do is to never stop moving and to collect the power-up in the first upper-level chest. As far as I can tell, it sometimes doesn't appear, meaning you have to restart the run.

Part 2: The wave of enemies.  I don't have names to refer to the enemies as yet since I couldn't find any that were official, so I'll try and avoid talking about any specific enemies. The key with this section of the level is memorizing the order that the enemies appear and trying to kill them as fast as possible since that makes them appear as fast as possible. A super could be used near the beginning of this section since you could easily get one again before the bridge, but I couldn't find a good use for one.

Part 3: The bridge just after the wave of enemies. This and part 3.5 are the areas where I lost the most time in this run and are in my opinion the hardest. The bridge consists of trying to cross it with as few slowdowns as possible, though this can be hard because so many enemies are thrown at you while you are on the bridge. Usually, it's wise to use a super at a specific point on the bridge since it gets rid of a lot of enemies and it's easy to get another super before the boss. There is also a power-up on the bridge if you managed to lose yours and for some reason, you want to continue the run.
Part 3.5: The area just after the bridge but before the boss. From what I can tell it's best to take the lower route and jump up, which allows you to avoid the flowers, which are very difficult to get rid of or pass quickly. It also avoids having to jump up the stairs, meaning you have to jump up the bottom rocks and then immediately up the top rocks instead, avoiding all but one enemy (the ninja? idk if that's the name but one runs at you right after the bridge that you have to kill). After you jump from the rocks, it's fairly self-explanatory until you get to the boss. Just keep going forward.

Part 4: The boss. The boss isn't very challenging, you just need to beat it fast enough that you don't get swarmed by the cat skull things. A super is used here to deal a lot of damage to the boss.
EDIT: It looks like the best timing for this super is right before the boss would usually shoot at you. The super overrules his attack, so you don't have to dodge the shot. 
THEORY: using the super could be better since there's a point (at least in my experience there was) where the boss backs up, and I think if you use it at the right time then the super could be inside the enemy for a longer period of time as they back up with it, making it deal more damage and the fight shorter.

From what I've seen so far (on December 13/14, 2020, only a couple of days after release) this is the fastest way to beat level 1.