There are 5 different elements to this achievement and each element is represented by a PGR3 in game badge.
To check what badges you have already unlocked, from the PGR3 main menu go to the achievements section and select badges and then use the right trigger to go across to the online badges section.
All of these badges can only be unlocked in the online career mode for the achievement to work.
You will need to unlock the following badges:
50 Online races: You will need to race in 50 online races in the online career mode, you do not have to win 50, or even finish in 50 races, if you fail to finish it is fine, but do not drop out as it may not count. For each of the race modes it has a list of the number of times you have attempted and won each race. Once the total of the attempted races is 50, the badge will unlock. The quickest and easiest race is Gotham Duelling, it is 1 on 1 racing so the easiest to find an opponent and the races are only a few minutes long.
Start Last/Finish First: From the starting grid if you are the back car just win the race to unlock the badge, this is very easy to achieve.
3-event win streak: Win 3 online career races in a row. Once you have won all the other online career races, just keep searching for Gotham duelling and try to win 3 in a row. If you have some friends playing with you, you can help each other out with this.
Clean Race: Finish a race without hitting any walls or any other cars, you dont need to finish the race, if you fail it the badge will still unlock.
Win Each Scenario: There are 8 different races you need to win Breakneck Racing, Nurburgring F1 Challenge, Speedway Skirmish, Knockout World Tour, Nordschleife Drivers Club, Urban Rally, Gotham Duelling, and Dusk Til Dawn Racing. It will display the number of times you have won the event so make sure you have at least 1 win for each scenario.
Most of these scenarios require 4 players to start and there is virtually no online community any more so if you are going to try to win each scenario you should try to find at least 4 friends to help you. All go into an xbox live party and search for the same game type. The matchmaking is pretty poor in this game so just sit there until the game moves you from your lobby, eventually you will all be put into the same room. This can take a lot of time so if you want the achievement be patient.