The easiest, and quickest, challenges for this achievement are:
In 1 Life:
Get 10 kills with a single weapon
Get 25 Bonus Xp - doesn't matter which events, just 25 overall, easiest is probably Beat Down, Assist, and Heal, if you are under 1800 exp
Get 5 xp w/5 different backpacks - one kill per backpack should do it, maybe 2 to be sure
Get 50 total xp
Get 1 kill w/5 different weapons
Get 15 different bonuses - not possible before 3650 exp, since that is the point that you will have 15 different events unlocked. It's probably better to wait till 4550 xp so you'll have Stuck and Headshot unlocked to take the place of things like Crush, which is fairly difficult to get done.
Doesn't need to be done in 1 life:
Get 10 kills with each weapon
Get 100 exp with each weapon - for things like Rail Driver and Thermobaric Rocket, do a Custom match with those put in as the starting weapons
Get 100 exp with each backpack
Now, that's 9 events that you could do. You could easily sub out the 1 Life: 15 Bonus Events challenge for another. But since you'll have to do it anyways at some point, best to get it out of the way early on.
The easiest way to do this is to set up a custom match, with Infinite Ammo & Enemy Locator tags turned on.
You can check how much you have left to do by looking at the Statistics page. It'll tell you how many kills and exp you've gotten with each weapon and backpack.