When the mission starts you will be in Love Fist's car. You can not get out or the bomb will go off and you will die/fail. You have to drive and keep your speed up so the detonation meter stays down. If you slow down too much or stop the meter will fill and the bomb will go off. Try and use the sidewalks/sides of the roads where there aren't any cars as much as possible but don't hit any poles/light posts.
I recommend driving south then curving left and then turning right to get on the main highway. Drive straight south until you reach the last bridge. Turn left onto the bridge and cross. Once you cross drive straight north on one of the main roads on the east island. Not too long after you cross the bridge Love Fist should defuse the bomb. Once that happens all you have to do is drive them to their event. After a short cut scene the trophy will unlock.