There are two local universities in Singapore that you can pursue biosciences at. They are NUS and NTU. Both offer PhD, and will usually give a small stipend of a couple of thousand a month to live off, in return for having you do teaching duties on campus.
Please don't take offense but I would ask you to consider what you are looking for in a graduate research degree, and why Singapore.
Usually someone chooses a location to do a PhD because the school has a strong international reputation or one of the three best professors in the world for that specialty is there, or the industry lead by research coming out of the ecosystem supporting it in that city.
At PhD level it matters who you worked with and the experience you gained.
Some good starting points for you are:
http://admissions.ntu.edu.sg/graduate/R ... fault.aspx
http://www.nus-edu.com/oam/
http://www.a-star.gov.sg