I keep randomly failing Thames Chase.

The first time, I was near the end of the level, at the staircase that leads to the street with the entrance to the subway. I shot and killed one of the black ops-looking bad guys and it tells me I failed because I killed the female assassin. Then I played again on a higher difficulty level, and I'm at the area just before the street with the subway entrance, where the ship is docked. There's one enemy on the ship hiding behind crates and shooting, and another shooting me from the window of a building across the water from me. After I killed them both, it tells me I killed the female assassin and failed.

What exactly is happening? Is she getting herself killed somehow because I'm positive it wasn't me.