Generally speaking:
1. Run like heck, and don't even try to engage monsters.
2. Being able to quickly place platforms is your friend. I'm not sure this is possible on most platforming difficulties without the keyboard and mouse combo.
3. You need to have enough of a lead on the lava that you can go down a few wrong turns, because those do exist. The trick there is recognizing them when they happen and scooting back down fast or using storm dash if it's horizontal. Every second counts, even when you think you have lots of time.
4. Greater teleport is another way around the dead end problem, although it comes with risks of its own; because of the mildly maze-like nature of the missions, if you teleport through a wall that seems to lead up but really leads just back down or is a different dead end, that's extra tricky. So keep a general eye on the layout as you're making your way upwards if you're planning to teleport through walls.
Hope that helps!
Actually I've found it very easy to place platforms even with the controller setup. The default placement really does work pretty much perfectly MOST of the time, unless I'm trying to move really horizontally.
Another tip I found good, using a Cloak enchant; so you can see where enemies are as you go up, and it might stop them from attacking and getting in your way as much.
