For Princess Tenko, try moving in a diamond.
........R
.....................P
The first time will require a bit more distance. Once she shoots, run to the bottom of the screen vertical to where she was.
She'll appear on you, but you can't die from her touching you. You're still not in the pattern yet, so go to where P is here, but be careful.
........Q
P..............T
........R
Then when she shoots, quickly move to where Q is. Then when she appears on you, shoot for a little bit and quickly go to T. Quickly move back to R afterward making sure to not get walled between the attacks. Repeat the pattern. As long as you move around in the order R, P, Q, T, it's not hard to keep the pattern in control long enough if you don't move too far.
Not exact of course, but hopefully it gives an idea of how it works. Also, the attack gets faster as time goes on, so try to end it quick.
Okay, Cranberry Trap. My record on this is horrible. Also, how do you succeed in the last 10-15 seconds of Flandre's Survival?