*** 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). You need 600 EXP to earn Icon status.
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 in a reasonable amount of time and, for Deathrace, without missing 4+ gates.
Once you learn the courses, it can become very easy to beat up on the noobs, and most players in the Race gametypes are noobs. This is also a good time to get your win-streak achievements -- I had 3 6+ win-streaks, all of which were in races.
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.