Well, the mission objectives tracker wouldn't work too well for keeping track of the double jump since if you're looking for it you'd probably forget to hit the next attacks, and the combo would drop. Which is actually a pretty decent reminder that you have to hit the next attack right after starting the double jump.
For the Spider-Man mission, try doing the chain parts as quickly as you can. That gives you extra time to input the shoryuken motion. As for the hyper finisher, you just need to input that as soon as you get that additional hit after the shoryuken. I'm not sure if you need to cancel from the second hit or not, but the hyper doesn't otg so you need it to connect on the initial bounce.