This is one of the more difficult trophies since it is based quite heavily on luck. Playing on the hardest difficulty and destroying the respawn beacons will increase the chances of legendary weapons dropping, but there is nothing you can really do to make this come faster. Eventually you will find a level 30 legendary weapon of each type. Once you have them all, equip the weapons and fill the slots on each one.
Equip every weapon and equipment slot with at least a level 30 legendary weapon or equipment