Outside, approach Thomas Hickey who is sitting on a fence.
Start by killing the lookout who is just in front and above you. Loot its weapon
There are more guns in the racks if you need.
Engage the targets that are being distracted by Thomas and Charles
Shoot some more guards, including once near the entrance
Then shoot the Powder Kegs near the wall, under the cart. See here for help: Assassin's Creed III: Johnson's Errand Shoot Powder Kegs
Kill the bandits that show up. Leave the fort with the chest. Loot one of the bodies on the way.
Defend Lee and Hickey. Be sure to keep them over 50% health so to complete the optional objective.
Stay close to Lee and Hickey. If you wander too far, you get the message: "WARNING: Remain in the area"
Shoot guards that are standing on the roofs of the houses. If the bandits don't fall down from the roof, climb up there to loot their bodies.
Once you defeat all the mercenaries, go to the green objective marker to complete the mission and leave the area.
This will complete the memory, "Johnson's Errand"
Kill mercenaries using firearms - 0/10 (Optional Objective)
Shoot the Powder Kegs (If you are having problems with this step, see here: Assassin's Creed III: Johnson's Errand Shoot Powder Kegs)
Do not let Hickey or Lee lose more than half their health (Optional Objective)