Assassin's Creed 3 – The Homestead: Achilles

Manor Mysteries 1 (Sequence 7)
At some point a Homestead mission will become available inside the Manor itself (once you have Norris on the property). Head in and over to the right, into the dining room. There you will find Achilles. He will ask Connor to follow him downstairs. He tells you there is a chest that he wants retrieved from a blocked Cve. Norris is to go with you to get this package so he can clear the stone. Once Achilles finishes talking, leave and Manor and head over to Norris, who is now marked on your map.

Once inside the mine, the two have a quick conversation. Now simply follow Norris as he heads for the cave. The two talk of the Huntress, Myriam. Norris will reach the cave, plant the explosives and move back. Then he will tell Connor to have the honors and blow the cave open.

Once inside the cave start running. There will be some partial collapses and Connor can slide under them if he has some momentum. Just keep to the left and it will no problem to get to the first marker. Once you make it there turn to the right and climb up to the ledge above. There is only a faint trail to get you started up but the rest is easy. Once you are up, turn to the right and hop across to the opposite side with the rock landings. From the second one, jump to the right to find a swing that will get you the rest of the way across with some help. Once there start running forward to avoid any nasty surprises. At the very end of it you will find a chest that needs to be picked.

Now you have 2 minutes to get out of the cave. Turn to the right, where the crows are and jump over to the thin ledge there. Shimmy to the left. Keep going to the left and Connor will take care of the jumping from stalactite to stalactite. After the pair, start climbing up and to the left. Head to the left and drop down from there. Run forward to the left as the passage right will collapse in front of Connor. Now weave through the cavern, going left and right to find the path. It is not too hard to make it out in time even with a few bad times. Once you make it out you need to get back over to the Homestead. Either call your horse or just run it.

Manor Mysteries 2 (Sequence 9)
Talk to Achilles inside the Manor after doing some of the Homestead missions in Sequence 9. He will ask Connor to head to New York and head to the Western portion. There will be a marked ruined building that he must find. Climb to the top of the building and there he will find the painting Achilles sent him for.

Legacy (Sequence 11)
Only accessible if you have let Father Timothy establish a church in the homestead. Talk with Achilles then head to the chapel and talk with Father Timothy.

Achilles' Painting (Sequence 11)
Inspect the marked painting inside the manor. Just enjoy the scene as you will have now finished all of Achilles' missions.