Yes, you definitely need a masters if you want to be a clinical psychologist. You can still be a psychologist with a first class honours degree and some work experience, but most will prefer a masters degree. It takes about 6 years to get a masters. A diploma in psychology is useless, you will definitely need at least an honours degree in Singapore. However, if you practise in other countries, they require at least masters (with US requiring a PhD/DPsych).
If you have the resources, I suggest going to Australia to do your education and training. The psychology field in Singapore leaves much to be desired... and only NUS offers masters of psychology. You can also do it through James Cook Uni Singapore campus if funds are a bit tight but you will need at least A levels or a diploma to apply. Not sure if private diplomas are accepted. http://www.jcu.edu.sg/