War Games weekly challenges 01/14 - 01/21
The Pistolero: Get 15 kills with a Secondary Weapon in a single match - 6,100 XP
This one's tough. The best ways to get this are SWAT, infinity slayer, and objective games particularly capture the flag.
The boltshot is the best way to do this, but it's tough to get good at it. Other than that you could always try switching out your primary with a plasma pistol and have a magnum as your secondary. Try shooting a charged plasma pistol shot and then changing to shoot with a magnum, noob combo style.
Raise the Flag: Win 45 matchmaking Capture the Flag matches - 4,750 XP
Wow, really? Aside from hardly being worth the time, the only way to get this challenge is if you already have the intention of playing capture the flag all day every single day. This is an obnoxious number of wins to get for a week, especially in such a time consuming playlist. In fact, this is dramatically more than half as many wins as the monthly challenge.
If you want to get this somehow, you'll need a team, and a good one at that. Or you'll need a lot of time too.
Either way, just get the heavy weapons as often as possible, and don't let them score. Throw grenades at their flag if they're camping and try coming in from different angles every time. Do anything you can to throw them off balance.