I wanted to update this forum as my husband and I recently used these posts for guidance...
Based on the advice we saw on this forum, we originally tried to find an air mattress in Giant at Suntec City (Carrefour has shut down and left Singapore altogether I believe), but we were told that they didn't stock any. So in the end we bought the Coleman camping air mattress from Takishimaya (double mattress and battery operated air pump for S$120).
However, within a week the mattress had died on us (and no we weren't on it at the time!). The folks at Takishimaya fixed it for us; we originally asked for a full refund and they chose to ignore this and fix it instead (it's only when I demanded the money back did they give us a credit note - something that's all too common in Asia; no one wants to give your money back).
Anyway, with that mattress out of the window, we thought about trying the Giant in Vivocity, which coincidentally sells a variety of air mattress brands. We settled on two single Bestway Comfort Quest mattresses (S$59 for 2, with inbuilt air pump), which have outlived the Coleman mattress and are much more durable and made out of thicker material. In comparison, the material used for the Coleman mattress is probably just thicker than what you might expect to see in a lilo!
(As an aside, Coleman have a cheaper/diffusion line, also sold at Takishimaya, called Coleman Go or something to that effect. I wouldn't even bother with this given my experience, but who knows, maybe you'll be fine...)
If you do want a foldable mattress, Seahorse sells one (probably north of S$100-150), and I'm sure Ikea does too. These are more expensive options compared to the air mattress route but I guess it will last longer.