I finally got an actual good time with really good execution :D
I think I had a pretty clever route too:
Improved it!
Regular route to get to sword and out, but I skip the gun and go to the shotgun. Use the momentum from the first drop to go far and do a skip to leave early. From the exit, I use the momentum to get to the clouds and climb until getting the grenade launcher. From there I go to the right side (although left is probably faster) and skip the rest of the level.