A quarter turn actuator - non electric - would most commonly be air operated, but exists also as water hydraulic, oil hydraulic or gas operated, or combined (for instance gas over oil).
I also assume that you are exclusively talking about shell pressure testing, not surface or complicated material testing for larger welded or casted more complicated constructions for special purposes. This is another matter.
If we use air operated as the typical form, this would be a part of a combined tubing/pipeline, valve and vessel contraption or 'plant'.
As such you would expect the 'shell' to be able to operate at the design pressure for the whole combined 'plant'. If this pressure is not given, at least the shell should be able to operate at the maximum allowable pressure for the weakest, most common part. This would probably be a valve, possibly again the solenoid valve.
Most European air actuators and common solenoid valves in air circuits are designed for a max operating pressure of 10 bars. (Compressors can often give more, but air tanks are normally regulated to set pressures at 10 bars).
If you do not find any particular test for actuators, it would be reasonable to test an actuator the same way as a valve.
A normal valve is most commonly body tested at about 1,5 times operational pressure. You do have a complication here in the way that valves normally are tested at 1,1 times pressure for seat leakage, and that the seat here (piston sealing or other type) would require to be able to withstand the whole pressure (1,5 times operational).
In this logic you will end up with following test possibillities:
1. Actuator producers standard or valve factorys standard for pressure and operational test with ( absolutely preferably) or without valve.
2. As valve operational test at about 1,1 times mawp.
3. Shell test at about 1,5 times mawp and operational and leakage over seat at about 1,1 times. (With valve!)
4. Test as required for air tank/vessel.
The number 1 or 3 seems the most sensible ones. Actuators should always be operational tested together with valves!
Remark:
In my experience it is not the shell pressure withstanding capacity that is the critical part of an air actuator. Normally the actuator is oversized mecanically compared to pressure, as you would also require the construction to withstand the mechanical torque.
The torque forces could under circumstances be considerable, and test for torque would not be practical, and you would probably have to lean on mathematical calculation of forces for this.
I have seen cases where actuator is OK but yoke or bolts or adhering forces to yoke or valvetop have been unsatisfactorily and parts have been deformed.
Under operation the 'first to go' on a valve/actuator combination is very often the actuator piston sealing, or actuator stem sealing, depending on construction.
In addition to a sensible testing, including operational test with valve, and a specificational requirement of a large number of operations without change of sealings, my advice is to put some consideration into purification of operational fluid (air or other) and quality on sealings and adeqaute choice of actuator size to prolong maintenance-free operational time.
To further prolong total operational time actuators should be equipped with adjustable endstop, and actuator or solenoid valves with throtteling devices to adjust operational speed.