This one is gone October 3rd, 2022 and may be the easiest actual racing one in the game based on my unlocking it yesterday. A Rallycross race has to be one of the daily online competitive events and they rotate so it should pop up once or twice more i'd imagine.
Since you only get one, maybe two more chances, I highly encourage you to see what course and car are required and practice just to know the layout. Race easy making sure you do one joker lap, don't get penalties, don't go off course, especially cutting corners, and don't crash. I raced hard and came in fifth, .5 behind the winner. I thought no way I'd be top tier, but I was in the top 5%, maybe higher. I'm guessing the majority of low scores are due to cutting, causing crashes or joker related penalties.
The achievement doesnt pop until you go into the competitive section after the event has ended and claim your prize. Also, DON'T HAVE AN INCOMPLETE WEEKLY OR MONTHLY EVENT RUNNING WHEN THE EVENT ENDS OR IT WON'T ACKNOWLEDGE THE ACHIEVEMENT. Or so I've heard. Best to be safe.
EDIT: Turns out the server closure was incorrect and servers stayed open. I would recommend getting the online portion done soon though. EA is closing a lot of older Codemasters game servers so it's only a matter of time and these aren't hard.