(Clearly not everyone has the same definition of "tricky jump".)
My record time for LPChip's
Learning to Jump is a little over seven minutes.
Go look at it in the editor. (Speaking of which, that level is very good and will indeed teach you how to jump; I recommend it to everyone who wants to get good at Very Hard and Lunatic levels. It's in the archive.
www.knyttlevels.com)
edit: Does it matter which order I do the various pathways in "The Deep Halls"? I'm leery of using a savepoint, only to find out I've locked myself out of another path / missed a powerup / etc. I've explored a room or three along in each direction, about as far as I could before dying & respawning back at the beginning of the area...
Firstly, see here.
http://www.youtube.com/watch?v=m7-6I_QjhSM Note that you can save by pressing down while holding space, even in mid-air. To travel to screens you still can't get to, teleport into a wall and hold the opposite direction to the one you want to go in. In levels that include a map (this being a KS+ feature), doing the same thing on the map screen will teleport you to the screen clicked on; this is practically essential for enjoying
Azure Serenity, given how big it is.
Secondly, I went right back to the beginning at least once while playing. Moreover, after viewing an ending you can warp to any of the non-secret zones of the temple. The only two places I recall that can't be returned from fairly easily. The first is the third floor of the Deep Halls (look for air currents at the bottom of the screen). On the left side of the level there's a barely-jumpable gap that leads down to two rooms with almost nothing to stand on, the lower one being fairly tricky to get through; you can't go up the hole again once you've fallen down it. Going down on the right side of the level leads to a lot of staircases that allow biderectional passage.
The second one-way part is in the third zone. At the bottom of the huge room with the volcanos, you can go either right or left. Right leads to a closed loop of screens and a needed item, while left leads to a branch. Going down in the first room to the left requires the umbrella; getting up to the top again involves a long loop of the hardest challenges in the path to the normal ending.
A tip: in the red room with the scrolling laser after the room with blue-key blocks in the floor, go left first for a savepoint. You may encounter temptation to return to the right, but go up twice an poke around before you do so.
Two items are available, one of which is extremely helpful for the return trip.