The page below of our Assassin's Creed 3 Remastered guide contains a walkthrough for Something on the Side and its optional objectives.
To begin the mission, use fast travel to get to New York and afterwards follow your contact on a horse.
That way you will reach a marketplace, from where you will have to follow the mysterious counterfeiter.
Follow them while hiding behind groups of people and edges of buildings.
Optional objective: Perform a successful static eavesdrop.
At some point the man will meet with his associate. Run up the stairs on the right and hide behind the above barrel. From there you will be able to eavesdrop on the whole conversation without having to move. That way you will complete the optional objective.
Optional objective: Perform a successful mobile eavesdrop.
Keep following the counterfeiter until you reach the place of the second meeting. This time you will have to follow the two men without leaving the eavesdrop circle. You can follow the targets just like before, but while staying inside the circle all the time.
Optional objective: Do not tackle or shove anyone.
Eventually you will reach their hideout, where you will have to chase Hickey. What really matters here is the beginning. As only the cinematic ends, quickly press the free run button to free yourself of the battle. Afterwards keep it pressed down and turn into the first (!) street to the left (instead of chasing Hickey, it's better to outrun him and block his path).
Afterwards head to the second alley on the right and turn left.
Behind the second wooden stairs you will have to once again run right.
At the end of the street you will see an indoor market. Run around it from the left side and wait for Hickey there. When he appears, catch up with him with the free run button pressed and press the attack button to knock him down. Unfortunately this game element isn't done so well and sometimes Connor might not react at all. Therefore you should try to be as close as 1-2 steps behind before attacking him. If you're in front him, Connor probably won't know how to react. The path described above is one of the easiest ones and will let you avoid bigger groups of people. Only by not hitting any pedestrians will you be able to complete the optional objective.