There are no such criteria except through the Global Investor Programme. The GIP requires a minimum investment of S$2.5 million for consideration. PR decisions are still entirely discretionary even then; this is not a vending machine.
The PTS Scheme considers “economic contributions to Singapore.” The government is deliberately opaque, but a reasonable, broad interpretation (since they also explicitly demand the tax records) is that direct income tax payments (plural — years) and unique or at least special talent-related contributions figure prominently. Tossing S$100K into some Singapore Savings Bonds likely isn’t going to mean jack s**t. Five years of S$30K/year income tax payments, nicely rising with salary increases, from a well known engineer with a patent or two who is greatly helping her local employer export some new biotechnology made in Singapore to several other countries.... OK, maybe then that PR application gets a second read and rises to the top of the endless pile. As an example.
Anyway, if you’re going to try to buy your PR with money, that’s the GIP. That’s the only way to “buy” PR, and even then it’s not even close to guaranteed. Otherwise, work hard, pay your taxes for at least a few years, do at least your part to make Singapore an economic powerhouse (leading to more and better jobs for Singaporeans), stay out of trouble, actually live in Singapore (working from your laptop from your grandmother’s house in Other Country X an average of 7 months per year total probably isn’t going to help), and then try your luck with the PTS Scheme. Or fall in genuine love with a Singaporean (opposite sex only, sorry), marry, have some children, work hard, stay out of trouble, and try your luck with the Family Ties Scheme. Always file a 100% truthful application. (Lying has to be deadly, one can safely assume.)
There are no “inside tracks,” no secret unlocking invocations, no magic words, no b.s. This isn’t like getting some government permit in a third world country where corruption is rampant.
Good luck.