Whilst I don't wish to detract from Lee's informative comments, any potential candidate would do well to understand the politics of pilot selection in SQ.
A pilot in SQ is an ambassador for the nation, unfortunately for the government the majority of pilots are not graduates. Even though they may be good at what they do, they don't follow the government line.
I know that the Straits Times is discussing the viability of GLC's and the likeliness of their slowly releasing their grip on Singapore, but there is still a very necessary [sic] reality that it is only "talking cock" at the moment. Now that there are government scholars in positions of power, it is likely that they will want like minded and suitably qualified individuals to join the "team". This will be manifested by bureaucratic and academic emphasis, maybe even military biased, where it is better to "fit the profile" than be keen to fly aeroplanes (and maybe even be good at it.)
Don't give up, and if you're young enough, do whatever it takes. The job, whilst diminishing in prestige and renumeration every day, is still a place for the passionate.
In fact the way things are going, it will only be the passionate, non graduates, that will be attracted to the job in years to come.