If you just want as many Legendaries as fast as possible there isn't much to optimize.

1. Kill every Captain on Sight. (Rarity does not improve).
2. Always Skip Time when you Fast Travel. (For fresh Captains).
3. Farm Nemesis Missions, preferable these with multiple participants.

If you want to farm a specific Legendary it gets a bit more complicated.

1. Search for Banners etc. of the Clan you want, the best indicator is a Statue.
2. Search for the Soldier type that can drop your legendary.
3. Let him kill you.

Make sure there is always a free Slot so the new Captain does not have to duel his way on the map which does not always succeed.