I beat the game with a time of 5:39.79 on patch 1.21.1. After multiple tries and some basic optimization I got here. Here are some tips if you attempt this yourself.
1. First we go to spongebob, on the way we pick up the 5 ketamine
2. After that go to patrick to activate the 4 murders
3. Do the four murders, drive there with your car (don't run over the enemies), then run back to patrick then go to squidward 4. Activate Squidwards quest and run to sandy to gain access to the chum bucket.
5. Go to chum bucket and run past the enemies, grab the key and open the boss room
6. Hope for the best, when the cutscene finishes, the speedrun is over.
TIPS: Use your ketamine wisely, right before driving and right before cutscenes will save much time. Always keep a car with you or know where the closest one to you spawns.
Dont focus on the bucketheads, just avoid them at all costs and train them like its COD Zombies. You only need 5 base ketamine, after that use all the ketamine you can to get the fastest time possible.