This is ship based combat. Whilst not a huge ordeal, having upgraded shields/hull and missiles will make this much smoother.
There is an imperial base in orbit around Toshara, you are guaranteed to find a few TIE fighters to attack. Open fire, take your time and allow them to call in re-enforcements, start defeating TIE fighters as they come at you.
As your wanted level rises to 4/5 the empire will start sending Cruisers. Defeat these and it should jack your wanted level to 6, and a Raider warship will spawn in.
The raider itself is not massively problematic to defeat. If you have the loop ability you can complete attack runs from far out, fire missiles, speed past the raider and loop back and repeat.
Once you've taken the raider apart, you may need to jump to another system to have your wanted status cleared and the trophy unlocked.