Shim will work or try to re set scope to see if that will allow more adjustment. I like the mirror trick.
Look at the crosshairs. If the scope is optically centered, you will just see the reticle. If it is not, you will see a shadow of the reticle in the reflection.
To reset to factory zero, you need to line up the shadow of the reticle with the reticle itself. You can do this by adjusting the elevation (top) and windage (side) turrets. There is no particular way to complete this step. It is more trial by fire. Keep adjusting the turrets until the shadow and reticle are lined up.