First of all, you should have a design spec document which should definitely have:
- Input voltage range
- Output voltage (accuracy, tolerance and, if required, adjustment range)
- Output power (continuous, peak and other ratings at different inputs)
- Efficiency (may not be constant and may be given for different conditions)
- Ripple and noise limits
- Line regulation and load regulation
- Environmental conditions
- Protections with definitions of expected behaviour (e.g. OVP latch, OLP hiccup, OPP latch, etc.)
- Applied standards and regulations if required (This includes electrical, mechanical and chemical stress)
NOTE: These all apply to a PSU regardless of that if it's an off-the-shelf or a designed-from-scratch.
Then, you can validate the PSU according to the specified requirements.
percentage overshoot during load step
This is defined under dynamic response and dynamic response should be defined well-detailed. The requirements may vary depending on the design but generally, allowed percentages of overshoot and undershoot during different load steps (i.e. 0 to 100%, 100% to 1%, 1% to 50% etc.) with different slew rates (e.g. 1 A/μs) are defined under dynamic response. Sometimes settling time is also a requirement. But what you absolutely don't want to see is oscillation. In some case you may want to measure the loop response with special equipment.