Personally I think drilling acrylic with a normal twist bit (designed for metal, but commonly used for wood) is risky. They grab horribly when they get through, and it's too easy to crack a thin piece that isn't securely clamped.
I'd get yourself a brad-point bit, like Liam is referring to, and if you want to be extra safe go through until the center point comes out the back side, and then drill the rest of the way with the drill running backwards. Or just finish forwards but very slowly and with light pressure. Keep the bit cool with a spray bottle.
If the side of your skimmer cup is less than a 1/4", I'd drill the flat bottom of the cup, rather than the round side. It's easier to tap, and easier to drill. Less likely to crack. You may have to do the drilling from the top.