Dodgeball forces you to just dish out explosive kills. You can level Explosive Shell Expert and Explosive Expert in a few matches.
Any other mode is tricky. Just use an RPG or a Hammer kickback and hope you get a lot of people killed with it.
Good advice from TSD.
If we're ever lucky enough to get another hammer lab...there's a bunch of stuff you can level up very easily in that but I'm not holding my breath because most people seem to prefer the BMM rotations.
Play Team Objectives it's extremely easy to get Fire In The Hole during King of the Hill & Turf War.
Also it's very easy to level up on BMM #9 in general since most of the action takes place on the lower level, so always try to get the RPG at the start of the game you're almost guaranteed to get a Fire In The Hole if you know what you're doing.
Also use a Mega Bomb or Hammer as your KB on the current lab maps you'll be Gold in a day or two.