Do I have to complete each and every level, including the secret levels and "skull" levels, or just defeat the World 3 boss to be able to unlock more content to purchase in the Mall?

I've been creeping along very slowly in World 3 and was just wondering if I'd end up sighing like hell at the end.

The Mall unlocks are probably just beating the final boss. I can't say for certain, I did all the optional ones along the way.
 
The achievements specifically state you need to beat every level, however.

Good enough, I suppose.

Thanks and good.