Outside of Boston, you'll find a scout who will lead you to find General Putnam stationed just outside of Charlestown. After talking to Putnam, you'll volunteer to take out a couple of ships out in the harbor. Slide down the hill in front of you to find the city proper. As you run along the streets, debris will start falling from the buildings above and cannonballs will land in the streets. While you may instinctually feel that the rooftops are safest, in this instance they are not. It is better to stick to the streets and keep moving. This will get you through the city as safely as possible.
Do so without taking damage to meet a constraint. Just be careful when you get to the dock area because there will be red coats and while most will be running about, a couple of them will still try to attack you. Try to run past barrels to break line of sight and avoid being shot. Jump into the water and start swimming to ensure you've gotten the constraint.
Look for the ship to the right first. Jump into the water and swim around the far side of the ship (port side/left). Climb up on this side and slide towards the front. There are two guards that are patrolling in a circle on the deck of the ship so be careful when you get here. Wait for one of them to come over to the edge of the ship. At this point, pull him into the water. Wait here for the second patrol or locate him so you know where he is. You can either do the same to him or wait for him to come around the front part of the boat. When he does this, climb up and kill the two guards directly in front of you and then circle around from behind him to assassinate him. There are two more double guard groups to kill but neither can see the other so just come up behind them and kill them with two quick kills.
With all of the guards dead, check near the main mast for a barrel and use this when prompted to destroy the ship. When you've set it up to explode, jump off the back of the ship and make your way for the next ship. This ship is a little tougher so be patient.
Approach the ship from the same angle and climb up the side. Remember that you need to air assassinate a grenadier on this ship so be on the lookout for the men with the large green packs and kilts. From this side of the boat, you should be able to perform at least one air assassination. Be patient and you may get another. When you've cleared a few enemies, try and find a safe way to climb up to the top of the ship. From the top, try and find a grenadier that you can assassinate without others noticing and then drop on him to finish that constraint.
If at any point you feel concerned that you may have been noticed, jump overboard and go as close to the ship as possible. You could even swim around the ship to get away. Wait for the last couple of guards to separate and then take them out as well. When the guards are dead, destroy this ship the same as the other. Get off the ship and when it explodes, climb back on and use the mast to get to the top. At the top, fly the American flag.
With your mission complete, swim back to the harbor and you will automatically be taken back to the shore. Use the horse to return to Putnam and start the battle in earnest/listen to one of the most famous speeches during the American Revolution.
