Damageless is known to be a pretty rough category, but if you practice it enough, you'll learn to get the hang of it. The main issue are the following levels:
The only real hazard of this level are the first 8 snapdragons. Don't try to rush through the 2nd row of snapdragons, and unless you're a top player, don't try to jump past the 4th row of snapdragons (unless you want to risk having to take damage and loading a save).
A fairly straightforward level, where the main difficulty lies in the moving lasers. If you play perfectly (relative to Any%), you won't actually hit the lasers. If you do not play perfectly, you'll need to play close attention to not get clipped by any of the lasers. Also, be careful about the final elves. Make sure they are either killed or stunned before you try to pull the lever, otherwise they may cause you to make a pain sound, causing you to have to load a save.
This level is all about confidence. You'll need to practice a lot to get through the laser sections, but it is possible to do. The first fire vent section is easy: just run as fast as you can, and you will never get hurt by the fire vents. If you need a consistent strategy for the first laser section, you can get past the first laser section by doing a double jump on top of the laser decals seen on the wall, although you'll need to time this well. After that first laser section, the level gets significantly easier.
Be careful about the first halberd knight that guards the first button in the second prison section, he will hit you if you do not kill him.
This level is the hardest level in the run, but once you figure out the strategies for it, it becomes a lot easier. When you first load the level, instantly load the save it makes. This disables the milk soakers that are on the bridge, which will basically always hit you. Next, bait the first set of knights back to the start of the level. Doing this will break their AI, and cause them to stop spawning and attacking you.
From this point, you can do whatever you want to get past the bridge, then break the front of the door as quickly as you can. If you do not use the strategy used in top level Any% runs where they break down the front door in 4 hits instead of 5, you run a small chance of getting hit by a cowapult or a knight. Pay close attention to your health, and if you do take damage, load a save as quickly as you can.