Didn't see anyone mentioning this method on PSNP so I'll do it.
You can earn every online trophy by yourself with little to no hassle at all. Here is the session set up you want to use.
Event Length: Laps
Number of Laps: 1 (You can use two)
Maximum Grid Size: 3 (Important)
Max Number of Human Opponents: 1
Fill With AI Opponents: Yes (Important)
Opponent Skill: 0
Opponents All Identical Car: Yes
Car Class: Current (Choose this so you can pick the car to race on from your Garage)
Rolling Start: No or Yes
Qualifying: 5 min (This is the MOST important setting)
So what would normally happen with a race with A.I. enabled is that it won't start a race because it would need at least two human players to confirm to start the race, but when you have the Qualifying added to the event, it will start the event with only your start input. No other players needed.
Now there is of course that one spot for a random to fill but you shouldn't have too much problem to be by yourself in a public lobby.