How Do I Find HARDCORE Servers? PS4

It depends on how refined your search is. If you are looking for a specific game mode or map, then there may be no hardcore servers currently using either of those. 

You need to uncheck all your filters others than the hardcore mode one. I just had a look there from my PS4 server browser and there are at least 10 hardcore servers up and running which are reasonably well populated. 

All search options (and I mean all) are open. Including foreign servers and unofficial servers.