Claw tentacles of impending doom
A spotlight will dictate where someone will be grabbed from. When they get grabbed, jump onto the claw with them as they're picked up.
Bayswater road boss time
RUN! Run a lot. The massive contraption has some sort of strange gravity lazer which turns buildings into bricks then launches them either up or down, for one reason or another. The first bit of the boss is easy, just run and run and run. It'll never do anything to you, only buildings, so just worry about running, jumping and timing.
Eventually you'll come to a ledge which you cannot jump down from or you'll die. However, stand just back from the edge so you can run and jump onto the building as it flies into the air. As it comes up, jump on it and run across quickly.