10 Brutes in 60 seconds. The usual advice for this contract mission is to use smoke bombs and/or poison. Smoke bombs disable your opponents for easy killing, and the poison delays the start of the timer. (The countdown starts when the first Brute dies.) This video uses other strategies that let you kill everyone using only hidden blades.
Easy Method
Here is an easy way to finish this contract if you are not Notorious. There are 2 groups of 5 Brutes. One group stands, and the other group patrols back and forth along the bridge. When the patrolling group turns near the middle of the bridge, they are just outside the "sensory" range of the standing group of Brutes. Use this opportunity to kill a Brute (or 2) near the rear of the formation. The patrol will continue for a short distance and then turn around to inspect the dead body(s). Kill a Brute (or 2) when they turn around, and kill the remainder as they crowd around the dead body.
The group of standing Brutes will soon turn around, as they are close enough to the new dead bodies to notice them. Repeat the process.
Notorious Exposed Blitz
Hang over the rail so you can sneak up behind the patrol as they turn. Use double hidden blades to quickly dispatch the Brutes in this group. Since the other Brutes are too far away to notice, they will stay in formation. Repeat the process on the remaining Brutes.
Peace and Silence
This is a hybrid of the previous 2 clips. When I recorded this, I had intended only to avoid becoming Exposed. It turns out I wasn't seen either. (No yellow bars.)