Slightly Early Death
Before the scene starts, Lawrence Washington and his brother George (the George Washington?) are prestaged. You have to locate Lawrence to progress to the assassination. To avoid locating him, turn the camera away. Both him and his brother are invincible to regular attacks, with the exception of a special attack by an ax. Getting him this way is tricky though because the game turns the camera toward him when you start swinging down with the ax, starting the scene. I try to avoid this by getting real close and making the camera face down, but not sure how reliable it is.
Here's also a clip demonstrating that the game makes them invincible. https://www.youtube.com/watch?v=Q9t4yWhTALc
Blitz
The fastest way I found of assassinating the target is to fire with your pistol when he's in range. thinking it's possible to free aim and shoot from farther away.
Stunt
At the very start, climb up the gazebo wall Shay is leaning against, jump to the tree, and make your way onto the rooftop. The target doesn't get this close to the house when he loops around.