Anyways, a few weeks ago, I was polishing the rest of my Master Thief Sprints off (I'll say it again, most are quite sadistic) and when I came to this level, I noticed I had 24 seconds remaining at the end (most people that uploaded were closer to 10). I didn't remember the layout, and I jumped to the ladder (because I didn't know better at first) which skipped a fair size section of the level. Today, reminded by watching Mr100PercentGamer do this level's sprint (shameless advertising, watch his stuff), I decided to try and do it again. Unfortunately, I wasn't able to match my time of 24 seconds remaining and proves once again any accomplishment of mine comes down to dumb luck.
In short, using a chandelier above the vault, it's possible to take advantage of Sly's good reach and hook onto the ladder while jumping. Jumping angles, timing, and possibly how the chandelier swings are factors on the success of the jump. If done on the first few tries, it can shave off much of the time you would normally spend going around.