I Don't think being a Hardcore Gamer means to perfect, or an excellent player at any game, I've know casual gamers, who after a short while, get a hang on the game, and beat whoever introduced them to it (it has happened to me, both as the hardcore or casual side). you don't have to beat everyone, or anyone, to be hardcore, you could just play by yourself, all alone ,and be a real hardcore gamer (which is the saddest way to be Hardcore), but most "hardcore games are intended to be that way: a 1 player game, with the "CASUAL" multiplayer option.
all "pathetic connotations" aside; I think a hardcore gamer, like most have already said, it's someone who knows everything, the most, or something about the gaming industry, or at least about their company/console of choice, someone who's constantly trying out new games or hearing the latest about games.
A hardcore gamer it's someone who not only enjoys the fun a game it's supposed to be, but looks for an entertaining and compelling story, and most of all, a really long replay value. critiques or praises the game, and, as of late, borders the line of fanboyism with their biased opinions (which it's very annoying). There are Hardcore gamers, as (sadly) there're Hardcore Fanboys :/
Casual gamers on the other hand,it's someone, who plays, has good time, kills some time, and the goes about their business, not really caring or thinking about the game he just played, he just knows its a fun and entertaining "pass-time" activity. they don't care about finishing the game, completing it a 100%, or beating someone else's record.
owning a console doesn't make you hardcore, specially if it's the latest next gen console, it just makes you up to date with current trend. Just tell me: how many people bought the Wii for it's novelty? or the hype of it? you can't say that there isn't at least one guy who bought a PS3 thinking it'll be the next PS2? or bought a 360 just to get ahead of everyone.
If you bought any of this consoles, because you're expecting or waiting for the next installment of your favourite franchise, then you are hardcore...any new great game that'll come along it just plain luck for the hardcore.
just remember this: it doesn't matter how well you play a game, or if you play 24/7, on weekends or once a month, if you have bookmarked IGN, Gamespot, ar any other game site, then you are Hardcore...
heck.. if you're in this thread, you're hardcore