Keeping the keys pressed Instead of clicking for every move a key a single time you can just keep being on it to move into one direction. To change directions you can click on the key in the direction you wanna change at the same time as you keep pressing the old key. Helltaker will charge into that direction until you stop pressing, if you are still pressing the old key he we go back to the old direction. Note: opposite directions cancel each other out so you can only press 2 keys at a time. This strategy needs much training because the timing is way harder.

Key mashing Especially in high tier runs the fast skipping of the dialog is the biggest time save. I personally before starting the game multiple keys to enter via the new menu and "destroy" my keyboard by moving over them with my free hand as fast as possible. If you have a fast clicking speed on your mouse you can just keybind it to the mouse. Alternatively precission is also an option but getting the timing is quite hard, but for short dialog to get the fast dialog for the first demons or Lucifer its needed.

The Bossfight 4 Phases and all basically have 2 phases. The first is evading getting hit, this is important because you need all your health to make the fast chain destructions. Honestly this just needs training remembering patterns or just getting good at the minigame.

Then there is the chain destruction, the best strats are quite risky allways for the first levels its still quite easy but the later ones are a challange, at best you look at the WRs and try to copy the strats by continously resetting a partlevel. Or go for cheaper more save strats by skipping one additional damage and going in save.

This is all for the run, the solutions for every level can be seen in top runs or just googled i wont add it here. So have fun doing some speedruns!