You NEED to play Lone Wolves because most of the Achievements come from there. It's the only Free-for-All Ranked game on Halo 3, unless Bungie decides to make a different Gametype, and some achievements require it to be Ranked and Lone Wolves IS, in fact, Ranked.
Achievements required to be earned specifically in Lone Wolves (occasionally in Campaign or just Ranked):
Two for OneScore a Double Kill with a single spartan laser shot in a ranked free for all playlist (Online).5 Points
Too Close to the SunDestroy an enemy banshee with the spartan laser or missile pod in a ranked playlist or in campaign.5 Points
Triple KillKill 3 enemies within 4 seconds of one another in a ranked free for all playlist (Online).5 Points
OverkillKill 4 enemies within 4 seconds of one another in a ranked free for all playlist (Online).5 Points
Lee R Wilson MemorialScore 5 grenade sticks in any ranked free for all playlist (Online).5 Points
We're in for some ChopDestroy an enemy vehicle with equipment in a ranked playlist or in campaign.5 Points
Killing FrenzyKill 10 enemies without dying in any ranked free for all playlist (Online).5 Points
Steppin' RazorScore a Triple Kill with the sword in a ranked free for all playlist (Online).5 Points
Mongoose MowdownSplatter an enemy with the mongoose in a ranked free for all playlist (Online).5 Points
Up Close and PersonalKill 5 enemies by melee or assassination in a ranked free for all playlist (Online).5 Points
Fear the Pink MistKill 5 enemies with the needler in a ranked free for all playlist or in campaign.5 Points
Headshot HonchoKill 10 enemies with headshots in a ranked free for all playlist or in campaign.5 Points
Used Car Salesman Destroy a vehicle that has three enemies in it in a ranked playlist or in campaign.
MVPEarn the MVP in any ranked playlist (Online).5 Points
Maybe Next Time BuddyBoard the same vehicle within 10 seconds after being boarded in any free for all playlist (Online).5 Points