The main reason you have so much difficulty landing a job is because the professors are not imparting the necessary skills that employers want from you. To understand this problem, you will have to look at the professors themselves.

A lot of professors in the university live in their ivory towers and are either
a)ignorant of the needs of the industry or,
b)promulgating lies for their own selfish benefit.

For type a professors (theoretician), they themselves have not worked a single day in the industry to really know real demands of their industry. I consider this class of professor the clueless. They are talk about theories but have no clue about the practicality of the subjects that they are teaching.

The type b are the evil type, they know that the industry industry is saturated but they still go around touting that you are in the best course ever. They love to spin tales about employers will be lining up for your signature after you graduate. These evildoers conduct themselves in this manner to so as to populate their course with more students. With the increase in student numbers comes more grants for research, which in turn, leads to increase publication of research papers and finally promotion. They do not care if whether the degree is useful or not, they just want do the above mentioned to get promoted and all these is done at the expense of sacrificing the future of their poor students. I personally know of quite a few full ex-NUS and current chemistry NTU professors who can be classified in this category.

In our increasing interconnected world, manufacturing jobs for engineers are being outsourced to countries which can provide skill workforce at the cheapest price. Singapore with the increasing wages of the labour force, is losing out to China for pharmaceutical bio-engineering sector.

My advice to those with bio-engineering degree is to use your engineering training to switch field.

As for those who tout about joining finance sector, the hey days of massive hiring in the industry is over. After the 2008 financial crisis, the industry in undergoing a paradigm change and a lot of the banks freezing headcounts. With a potential recession looming on the horizon, I don't really think the banks will be increasing their overheads by blatantly hiring everyone on sight.

5 months without a job is a worrying situation indeed. In addition to the interest payments on your student loans, you have to also take into account the potential income loss for the 5 months that you are jobless. You might have better luck during this period (early part of the year) when people job hop after getting their bonuses. If you don't secure a job by April, you will be competing against 2012 fresh graduates by May. Another alternative for you is to apply to read a post graduate degree in a non-bioengineering discipline. Our government is very generous in providing post graduate scholarship to applicants with 2nd upper honours degree. I would recommend to all those who are qualified to go into water or energy related research. With your bio-engineering background, you can probably do a post graduate research in bio-based water purification process or study means to harvest the low molecular weight hydrocarbons from algae. Although the above mentioned examples may soud a bit outrageous, but in order to survive, you definitely step out your comfort zone into uncharted territories.