Hi fellow competitor!
I don't think the job market has improved. I'm in the same boat as you - I've been looking for biomed/life science jobs myself for almost 2 months and only had 2 interviews so far..maybe it's something to do with me being a foreigner :l
Try applying for the EPEC (Employment Pass Eligibility Cerificate) online, and if you are approved you can apply for a 1 year Long-Term Social Visit Pass (LTSVP) in order to stay here to find a job. The EPEC is free and the LTSVP will cost 30 bux. That's what I'm on now.
There is also this thing called a Landed-PR that you could apply for which makes you a PR once you find a job in SG (I'm guessing it will be easier to find jobs with employers who only hire citizens/pr). It will cost around 1500 (half price for recent graduates with no work experience) and the processing time can be quite long (3-6 months). You will have to find a consultant to apply for you - I think they were called SMC from memory.
With finding a job, I use sites like JobsDB, JobsCentral and JobStreet. You can also try googling science companies you want to work with and contact them. I'm not familiar with job pay but it does seem rather low (1700-2500) for graduates...senior positions will probably get higher pay.
Hope this info helps...and anybody correct me if I got any of this wrong - I am only speaking from my own experience as a newbie
Good luck with the job hunt!