Make your way inside and, when you can, up the stairs. After a quick chat, go up the stairs and meet with your second team member. William Johnson will be able to help you if you can find his research for him. After you talk to him, you can leave through the front door or stick around and pump Johnson for some background information.
Leaving will immediately drop you in front of a mercenary fort where you can find Thomas Hickey. Talk to Thomas and you'll talk about your plan for getting into the fort. You'll then be shown your first target and taught how to shoot. It is important to note that if you are out of the effective range of your weapon, Haytham will not attempt to fire even if you are aiming.
Shoot the guard and climb the hill to his position. Nearby, you'll find a rack of muskets. Grab a musket and prepare to start a fight. You'll see the red markers down below you. Do as the game prompts you to fire at one of the guards. When you do, your team will attack the remaining three and likely kill them before you have a chance to kill another.
There is a constraint for shooting and killing 10 of the mercenaries but for now you should keep to yourself and walk further along the hill. You'll see a group of mercenaries just off to your right, practicing. Shoot one of them, drop your musket and then shoot another if you can to start off the fight with a couple enemies down. This will also drop the musket, leaving you to use your sword and pistol, both of which are far more effective at the close range you'll be fighting at.
A fight will start between the mercenaries and your small band. You'll probably be surprised by the effectiveness of your team members who will likely deal with a good couple of enemies themselves. While there are likely only two more enemies on this hill with you now, more enemies will be at the bottom of the hill and come up. Even though your team is good, you should be prepared to fight them in case an enemy slips through.
When you've dealt with all of the enemies here, you'll automatically make your way to the gate further inside the compound. Use the LT/L2 button to take aim with your pistol or musket. You want to aim for the couple of barrels laying on the ground beside the wagon rather than the wagon itself. Hit the fire button (Y/Triangle) to shoot. If you don't shoot, aim at one of the closer barrels to ensure that you're aiming at something within your range.
With the gate destroyed, head further in to find the chest you are looking for. When you inspect it, a mercenary will appear with a couple of men. Aim at him and shoot him to start the fight. With him out of the way, there should only be two more enemies left. The two remaining enemies shouldn't be much challenge for the three of you. Take a look through the dead bodies for ammo after the fight so that you are prepared to shoot more mercenaries.
After you get a little ways past the gate, you'll be attacked by a few more mercenaries. Start the fight by shooting the first enemy and then get closer in for some melee combat. Loot the fallen enemies for more ammo and then follow your friends out to the road. As you walk along the road, you'll be ambushed a few times by mercenaries. Some of them will come out of the corn fields for melee combat but others will appear on the rooftops. The first group of enemies will come from the cornfields as you come to a wagon on the right side of the road. Kill them and pick up the musket that one of them drops. The musket has a longer range and will be more effective when dealing with the mercenaries on the rooftops.
From here on out, you can carry the musket and fight with it in melee range or you can use your closer range weapons and try to pick up muskets from fallen enemies as you need to for longer range combat. The latter option is definitely viable since all of the mercenaries on the ground will be carrying them but if you feel comfortable with using the musket for melee combat, hanging on to it will be the safer bet, especially since there's a constraint on ensuring your friends have at least half of their health left. If you carry the musket, it will be less time looking for a musket and more time killing enemies that are shooting at your friends.
As long as you've managed to shoot four mercenaries up until now, you should find six mercenaries on rooftops that you'll need to shoot anyway from here on out. This will make at least ten so you should meet the constraint. If you've been following along, you should have killed six or more enemies with ranged weapons.
After killing the last enemies on the rooftops and the mercenaries on the ground, you'll regroup with your men near a wagon and end the mission.
