There are two major keys to this level. One is the elusive 5-4 skip, and the second is killing Sluggy in only 4 shots. Both are explained in detail below. Besides that, this level has a lot of stairs and you want to be fast with them. The fastest way to move up stairs is to continuously jump, however you want to run for a few frames between each jump as the stairs give you a little bit of speed in the beginning, but then don't let you exceed that speed.
Minor time-save at the last stair section: 
This trick is the most saught after and prestigious trick, since it saves over a minute in a run if done.
The trick uses a long series of perfect flutters and then bats to regain height with extended flutters to skip the autoscroller, it gains its difficulty in being able to perfect flutter consistentently and manipulating the bats which don't do the same thing everytime.
The current warpless and 100% world records use this trick.
You can find an image based step-by-step guide, for help on learning the skip, here.
Sluggy 1 Shots
There is a way to kill sluggy in only 4 shots. This strat is very fast, and is very reliable with enough practice.
There is a 1-1 warp at the beginning of 5-4 that saves quite a bit of time. This video demonstrates the warp in real time and includes a description for a consistent setup (courtesy of Blkyoshi) for the warp. (skip to ~9:45)