You have to beat 10 Rivals, friends or not. After every race you will be prompt if you would like to play again versus a Rival which is usually pretty close to my time. No one on my friends list are into racing games (sadly) so it would always bring up a random Live user which are usually LESS than 3 seconds (but usually 1 second less) from my best lap time. I'm not sure if this is the case if you do have friends that play this game or not so someone will have to verify this.
What I did in every race, while set to EASY, is do pretty poor. Good enough to beat the CPU racers, but poor enough so that I can easily be matched up with someone I can defeat without too much work. After every match, I accepted the suggested Rival, and defeat it with ease. After 10 Rivals, the achievement is yours.
As per Yreon all of the Rival Events in Race Central count except for the Monthly Rivals. You can even race against yourself!
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Thank you and good luck!