To boost the 6,000 weapon kills required for the starting weapons, pistols, and so on, create a private game on King of the Hill with a required score of 240, set the number of round wins to your liking, and select a small map. Playing three rounds on Thrashball, I received 150 kills in a span of 15 minutes.
For the various match-based medals, create a game on a small map (like Mercy) with the lowest point/kill requirements for winning. Turn the bot difficulty to Casual and select one round wins. I do recommend filling each team with bots. Killing one bot in Team Deathmatch 15 times while waiting for it to respawn is monotonous. Depending on the quicker game modes like Warzone to the longer King of the Hill matches, each match typically lasts between 1 and 2 minutes.
NOTE - The only known caveat to these methods is less experience than if playing online, but each new medal awards point bonuses.
Boosting Onyx "Doorman" Medal:
To unlock Seriously 3.0, every Onyx medal is required. The Onyx "Doorman" medal requires players to interact with 2,000 total objects during the campaign. You can obtain this medal by interacting with the same object multiple times. An effective strategy is to load up the first chapter, and keeping pressing 'X' next to the Thrashball table before you speak to Jace.