According to NUS, UEC students need to take their entrance exams for certain courses (I think Dentistry, Medicine, Double Deg Law and Economics, Law and some others)... which A Level, IB, STPM or most others do not need... GG for UEC being "harder".

NUS's website has some info. Some of its entry requirements - on paper (or on the internet), at least - do not look very high... for example, a lot of Engineering courses don't even require Physics at A Level (haters please check before rebutting what I wrote, it accepts Chemistry in Physics' place, and allows for O/AO/AS Level Physics as well). However, most people here claim it is very selective, so it probably goes through an arduous selection process. A school of its calibre should just require A Level grades A*/A in both Maths and Physics outright, like a lot of other schools do.

Look up specific subject/grade prerequisites (there's a big table for all the subjects and degrees).

After that it's probably 3 or 4 subjects with As (Bs might be excusable but I wouldn't know).