*** Sorry, folks -- servers are down, so this achievement is unobtainable. Original solution follows. ***
Easy to grind this achievement out, as you always earn EXP if you complete the competition (see below).
The formula for EXP is roughly as follows:
WIN = 16, 2nd = 12, 3rd = 10, 4th = 8, 5th = 6
Correspondingly, smaller matches will give you more EXP for last place.
However, you MUST complete the competition to earn points. This means finishing a race in a reasonable amount of time, landing a trick, copying a trick in SKATE, etc. If you fail the basic competition criteria, you will DNF and earn ZERO EXP.
As for gametypes, I would consider Deathrace to be the easiest match to win -- once you learn the courses, you can beat up on the noobs pretty soundly, and they are the majority of Deathrace competitors.
I probably had a slightly better record on Spot Race, mainly because the gametype can be a bit overwhelming for a noob. (A race with specified tricks in specified areas along the way.) That said, I also had trouble keeping people in the lobby for that same reason, so there was a lot of downtime waiting for matches.
If you're just looking to get into a match, there are a ton of people playing Spot Battle. I wouldn't expect to win any of these matches, however -- all I can say is that if you play one of these matches with a strong opponent, you'll see why. (I actually saw someone put together a 40,000+ point trick.)
As for the others, Jam and Best Trick are pretty good if you are decent at scoring on tricks. Jam is a faster match, whereas Best Trick is three rounds at 2 minutes each. SKATE, however, takes quite a long time, and can be dominated by the trick-setter. I recommend avoiding that gametype altogether.
EDIT: To check your EXP, go into "Xbox LIVE", "Community", "My skate. Profile". At the bottom, it will show "EXP Earned" and break it out by Trick, Race, and Total EXP.