There are still a number of tournaments being staged in this game (as of Jan 2010), around 1 a week.
However there have been mutterings that the servers may be getting shut down ... that may or may not be true, but if you are lacking this achievement it might be a good idea to try and get it.
The achievement is divided into two halves, with the first half (qualifying) much tougher than the second (turning up to the lobby for the first round race).
Generally speaking, after a number of attempts, I have found it easier to qualify in an event which features manual transmission cars. This might be the case because some are daunted by manual transmission and do not enter these races, but I qualified mid 30s for a manual transmission race recently.
In qualifying for the event, the first thing you should do is take a semi-leisurely spin around the track, noting its features, sharp bends, braking areas, straights and areas where you might be able to gain time through a good turn or by sticking to driving line.
After doing this and familiarising yourself, knuckle down and try to set a time.
Like any qualification period, your best time is highly unlikely to come on your first couple of laps. It may be 6,8 or 10 laps in. I've found mine usually come about 6-8 laps in - at a stage where I know the track, have worked out the driving line and braking points and have the confidence to floor it when needed without hitting a wall.
If driving a manual car, it is important too to note and memorise the gears in which to take certain corners, and when you need to gear up from 3rd to 4th (or 5th) and back down again.
This sounds tough but it is actually deceptively easy. Once you have these points sorted out, gearing up and down is easy and maximises the acceleration at vital points during the lap.
Lastly, once you have qualified, continue to check back to ensure you remain under the qualification time right up until the end of qualifying. You may qualify early but be nudged out of the top 64 by faster drivers, meaning you will need to improve your time through requalification.
Once you have qualified, simply show up in the lobby for the first elimination round - the achievement will pop. Then race and see how far you can get!!
EDIT - I've been informed in the comment below that Gotham Tv (and thus, the tourneys) may have been discontinued. Before you go to all the trouble of trying to qulify, investigate whether this is actualyl the case.