This is a solution for those who want to boost this (as there often aren't enough people playing this game to do it legitimately). You'll want to get at least four people in a group (eight or more is preferable, and twelve is the max) and search "Conquest." It's a gametype where teams must capture and defend three capture points marked "A," "B," and "C."
At the beginning of the game, everyone on both teams runs to the point at center of the map (usually "B") leaving the other points alone. One team captures the point (and everyone involved gets 400 XP) then backs up, and the other team does the same thing. Repeat this until the timer runs out. Done correctly, you should not get anywhere near the score limit.
Here's a video of me and my group doing it:
For those who want a breakdown of the experience gain, here you go (halfway is just after you hit level 19):
This will still take a while (several hours for all four classes), but it's still the fastest way. You may have to deal with a few randoms, but if you have a large party, it won't be a huge problem (and many of the randoms I ran into figured out what we were doing pretty quickly and just joined in). Stick with it, and this achievement will be yours.
EDIT: Two more things. One, if you jump a certain number of times in without dying (I think it's 50 times), you get a bonus called "Bunny Hopper" for an extra 200 XP, which you can get once per game (which isn't a lot, but it adds up over time). Also, if you pick up the Intercooler or Ultra-Power Core pickups and activate them next to multiple teammates, you get more XP. You can do this every time they respawn (every two minutes or so), but only one person in your group can do it at a time.