The solution is technically easy. Complete 20 online races. That's it! However, it is slightly complicated due to a ton of issues with the game actually registering completed races or not. --- Here's my solution to that. (Hoping it works and saves people time down the road)
For those wanting a tracker on the trophy... go to My Rider -> Titles (Title 79 will show how many completed as you need 50 to unlock that specific Title) and the trophy will Unlock @ 20.
Now onto the confusion of whether or not it's glitchy... is it? Yeah a little. But this is my understanding and it is 99.9% accurate from what I can see. If I can have more confirmations on here, I am hoping to bump this up to 100% accurate.
What counts and what doesn't.
Does NOT count if:
1. You get a NC (not completed) - this is given when you do NOT cross the finish line before the timer runs out, this means at the end if you are in 5th spot and you notice the 1st spot has crossed the finish line, there is a small timer at the top of the screen that pops up, and will count down from 40 seconds. You need to finish and get an end time before that goes to zero.
2. In a SINGLE RACE if you do NOT receive money from your pole position. If there is 12 players (or a mix, AI and players) you need to finish 5th or higher to receive anything. 6th spot, and anything below gives you $0.
It will count if:
1. You play through a race in a CHAMPIONSHIP race! ALL CHAMPIONSHIP RACES ARE COUNTED!
2. If you receive money from your position in a SINGLE RACE. You must receive something for it to recognize the completion. (5th position or higher)
PRIVATE MATCHES WILL COUNT, so long as it follows the previous four guidelines.
I hope that works for all of you and let me know if that's accurate or not. (It worked for me 100% but I can't speak on behalf of anyone else)