What would help is if you gave us some more specific info. Do you have trouble on all the parts or just one or two?
My most basic advice is not to worry about TMs too much, especially not the 10 second-er in the tower. Look for shortcuts, even if they're only small ones. For instance, after the start pad there is a small slope, which can help me jump directly to the first gem without having to use the steps nearby.
For me, the biggest obstacle to qualifying used to be the ice. You can either just use diagonal and a healthy dose of control, or you can do something harder but much quicker.
1) Right before you get to the ice, you should be overlooking the Helicopter that you used to pass through the hole in the wall.
2) Leap down on it, activate, and hit against the wall in front of you. Done right, you should be able to fly up to the gem on the ice.
3) Jump off the ice when you get this gem and you should be able to fly to the end.