Hmm.
I play the game to plot completion first. Easymode, whatever; just finish the plot. Some games, like TF2, have no plot, so I skip to achievement hunting.
If I like a gaem enough to go back for another bite, I go achievement hunting. Or otherwise just hunting down specific goals or quests; much like P3P; beat P3, now trying to do it better. I've suceeded, because I actually got Thanatos this time.
Now to get 100% and beat the true boss...