There are many paths in the Patents field.

You don't actually need a law degree to be a patent attorney (under the Singapore regime, formally called a "registered patent agent").

In fact, an LLB will only be a distraction. If you want to do hard science IP and patents prosecution, just go for a full fledged science background, up to advanced Masters or PhD lvl. You'll then need to take the Grad Dip IP (old GCIP) course which will teach you all you need to know about IP law, and pass the Patent Agent Qualifying Exams. Then you can be registered after training.

The value proposition of a lawyer who is also a registered patent agent is that you're supposedly the "bridge" between the more technical science-background PAs, and the "lawyer" side of the value chain. But if your interest lies more in science, just ditch the LLB part entirely and don't waste time with a Double Degree, cos you'll prolly be locked out of MSc or MEng degrees due to lack of depth.

If you want to be a scientist working in the patents field, get a PhD in whatever scientific track interests you and don't bother about the patent agent track. You can get a patent scientist job at an IP firm doing pure patent drafting, and leave the prosecutions part to the lawyers-cum-registered agents.

If you just want to be a vanilla IP lawyer, then take the LLB and all the various IP modules but chances are you aren't going to have much value without a hard science background