RE: scope on a side hammer
T/C sell rings and mounts for their various models. If you did not use them, that's what I would do first. Shims should not be necessary. One thing I might try is to switch your rings and/or mounts around, assuming they are "interchangeable" and not designated as front or rear.
If you are shooting high, the back end of the scope is too high. If you do use shims, make sure to shim the front end. Adjust your scope to the center of its adjustment range and get it hitting as close as you can by varying shim thickness. Then use scope adjustments for final sighting in.