For decorated solider, you would need a double kill or up, a killing spree or up, a splatter, sniper, melee, assassination, boarding a vehicle, and a stick. Zanzibar is the best place for it in my opinion.

And for rainman, you need to play EVERY Bungie-made gametype. Slayer, Team Slayer, Elimination, Swordball, Crazy King, EVERYTHING. Very annoying, but the best bet would be to create a server and invite friends to it.