Do I need to amend my return due to a Box 12 W amount revision on a W-2c?

Box 12 code W is your HSA contribution.  Since that gets reported to the IRS on form 8889, I would say it does need to be amended, even though it should not change your tax owed.

does not seem to affect the refund amount whatsoever when I looked at mine that was corrected for Box 12 code W. In that case I chose not to do amended return for it, especially since they don't allow e-file for amended returns.