The force of radiation pressure is $F=P/c$ for absorbed radiation or $F=2P/c$ for reflected radiation, with $P$ the power and $c$ the speed of light. If you want to generate 750 N of force, you need (a) a radiation source of 100 GW and (b) a mirror that reflects so well that nor the mirror, nor you will be vaporized in an instant.
Update: CuriousOne remarked correctly that you don't need a power source of 100 GW. Rather, use two mirrors to make a laser cavity with 100 GW of irradiance on the mirrors, but the actual power that you need to pump in is only a fraction 1e-3 or so for good visible or infrared laser mirrors, i.e. a sustained 100 MW. That's still a rather substiantial laser; I don't think they exist.
An alternative approach would be to use microwave mirrors, which can be designed to have losses on the order of 1e-6, or even 1e-9 in the case of superconducting mirrors. Microwave sources that can deliver high power exist (everyone has one in their kitchen). Taking an optimistic 1e-9 loss at the mirror, you would only need to feed it with 100 W of microwave power. A problem here is that low-loss microwave cavities are typically bottle-like enclosures, not separate mirrors.
For any low-loss (high-Q) cavity, the length and orientation of the cavity walls or mirror must be kept stable within very tight tolerances, which is at odds with the idea of levitating a human.