Working with plexiglas I would first use a small, sharp drill bit. Then work in small incriments up to the size you will need. Use something that is a "fine" drill bit. Too big of a bite and it will just break the plexiglas. That's been my experience with the stuff. Same goes for fiberglass. 

WOW, that must be why my bits worked. They're always dull....    Thanks Louis, I never knew that. 

That is why I recommended the slow speed.  When you drill anything you must use the correct drill speed and feed pressure for the best results. 

Dull Bit and Slow Speed will do the trick!  Sharp bits will dig into the plastic rather than shear it off. 

When I am working on Vistalite shells I use a Unibit step bit.
The Unibit offers several advantages over conventional split-points for acrylic. First of all, a standard or side fluted bit will grab the acrylic. These bits are built with side flutes to pull shavings up and out of a hole. A Unibit or step bit only has a cutting surface on the face of each step.....they will not catch the work and cause cracks. The single-flute design on the face of a Unibit, cuts with a scraping motion and does not want to pull suddenly into the work like a standard fluted bit does. Next, the Unibit has a slight chamfering edge between steps. By just drilling a hair into the next step, you automatically chamfer the holes, a must-do on acrylic, sharp hole edges can be a source of traveling cracks later on. The Unibits also have many sizes on one bit.
You should not center punch acrylic, I suggest drilling a 1/16" pilot hole with a conventional bit first on ALL holes to be drilled. It will keep the Unibit on target and essentially "walk" it through the shell wall. Don't use excessive pressure. Let the bit do the work. I have drilled holes for years on all types of acrylic shells and never spit or cracked even one. These bits cut acrylic like butter.
Here is a link to a Unibit.

http://cgi.ebay.com/Irwin-Unibit-2_W0QQitemZ150295777508QQihZ005QQcategoryZ50384QQssPageNameZWDVWQQrdZ1QQcmdZViewItem