Prerequisite: Make sure that you opened BetterZip 2 from the Mac App Store (MAS) at least once before upgrading. If you need to, you can re-download BetterZip 2 from the Mac App Store’s Purchases tab. Just make sure you delete BetterZip 4 before doing that, because the MAS won’t install the old version over a newer one. After installing the MAS version, start it once and quit again.
If you can’t seem to get it to work, simply forward me the email invoice you received from Apple when you bought BetterZip. I will manually generate an upgrade key for you.