Two options besides trading for one, as far as I know:
1) Soft reset your game at starter selection until you get a shiny one. Save just before the point at the beginning of the game where you would get your starter, then pick your starter, and hope it turns out shiny - if it doesn't, press L+R+Start and try again (it's quicker than going back to the Home menu and reloading the game).
2) Plop it in the daycare center with a suitable partner and farm eggs until you get a shiny. You'll need either a female starter (plus a male from the same egg group) or a Ditto for that, though. If the previous games are anything to go by, your chances are better if you have two parents from different parts of the world, like your English starter with a Japanese Ditto for instance, so I'd recommend hitting up the GTS to look for a parent from a different geographical region than you.
It really all comes down to being really lucky.