Is there a way to bruteforce the private key of this cryptocurrency altcoin?
First up: APC != APW. The later is a different fork, which you missed to follow… costing you cash. Besides that my research showed that the original APC coin site is down, 99.9% of its block explorers are down, and only the most exotic exchanges list APC (naming it AppleCoin, AppeCoin, AlphaCoin, etc. all using the same APC short notation) which are clear warning signs that the 2013 APC AppleCoin currency is down and out ever since they forked it into APW.

Answering the core of your question

Having said that, cryptographically the wallet recovery based only on public key(s) and wallet password is infeasible as it would mean brute-forcing your public keys to recover private keys. This is much harder (from a time &amp; resources perspective) than mining cryptocurrency, so thinking about brute-forcing is a futile effort.

The password you've got protected the database your wallet used. That's not helpful when trying to recover your private keys… unless you have a backup the wallet database — which you stated not to be available.

My advise: learn from the experience and move on… while constantly reminding yourself that regular backups of important data (all data, not only financial data) can save you from a lot of frustration and from losing money.