Cathay is the official shop for most everything, but their prices can be high.
In the same mall there are a couple of 2nd hand lens shops where you can find the occasional bargain. Also, in the Peninsula Hotel shopping mall across the road there are a few more. Camera Workshop is good if you speak to Daniel. The other old guy with the white hair tends to overcharge, especially if you're not local. Camera Workshop will sell new Canon lenses about 10% cheaper than Cathay.
In terms of bargains, you might find one or two, but I have found that KEH is often cheaper than any of them. I have a large collection of Contax Zeiss primes and most of them were sourced from either Ebay or KEH because the Singapore prices are just out of this world. It's almost the most expensive city in the world, so finding bargains there is a thing of the past. Back in the 90's it was better.
In Sim Lim Square on the ground floor there are a couple of pro camera shops near the outside, mostly Panasonic gear. Do your research and go in informed. Do NOT buy anything in Sim Lim Square without doing any research. If you want to pick up a reasonably priced Shotgun mic go up to Hung Brothers on the third floor and speak to either Jacqueline or Genghis (yes, really). Get cables made for it on the 3rd floor of Sim Lim Tower opposite.
Don't buy anything in Orchard Road. Not a thing. Nothing. Nada. Rien.
Bert's Lighting House might also be worth a visit. It's a bit hard to find and it's mainly rental, but he carries stock of some good stuff, including Parallinx
https://www.facebook.com/bertlightinghouse
Haggle everywhere. You will get charged 2-3% extra if you try to use a credit card. GST (VAT) is 7% and can be reclaimed at the airport if you are a tourist.