The basic formula used in analyzing thin-walled spherical pressure vessel is:
stress = PD / 4t
where P is the pressure inside or outside, D is the inner diameter, and t is the wall thickness.
therefore:
t = PD / [(allowable stress of the material) * 4]
Note that this formula is only applicable if D/t >= 10
Note also that allowable stress in acrylic is 10,000 psi @ room temperature. This changes when you submerge this in water, so might want to consider this too.
Edit: The unit of measurement in the formula is:
For English system: stresses should be in pounds per sq.inch (psi) while dimensions should be in inches (in.)
For SI system: stresses should be in megaPascal (MPa), and dimensions should be in millimeters (mm)