Let's see…(please pay attention Game Freak!)
1) Weather is random, like rain (eg some places it doesn't rain, but in the places that do, it's totally random and with the seasons), and whenever you're in a certain climate, you have the chance to evolve the Pokémon. Not being able to evolve Pokémon for one or two months is a drag (snow in the summer?!) but the sheer awesomeness (for me at least) would make up for that.
2) Trade, but only with GTS. That would be cool, though I can see people abusing that sort of thing like they already have.
3) Trade, between languages. If this is about "worldwide" and "3D" and "connected" and stuff, how about trading through languages? That's a way to unite the whole world through your games!
4) Battle a certain amount - doesn't matter friendship, nor level - if you battle "x" times, your Pokémon will evolve regardless. Seems kinda…what's that word ¬¬…oh right, relevant. Anyways, seems kinda relevant if the legendary theme is based on Nordic mythology. Not being racist lol, you have to admit Thor and Odin and all those people are kinda war-like for their part. Or any mythological gods, for that matter, just because.
5) Have your Pokémon faint a certain amount of times. Failing is another way to learn! Then again, PETA will be all over that…
I'm out of ideas.