Many of the levels are speed-based, and your most basic method for increasing speed is to angle yourself so that your afterburner is backed against a solid wall. When you do this, you'll get a push-off from the wall. You can't do this with the dotted walls, though; nothing will happen because the flame will go right through.
If you are having trouble getting up a wall on a high gravity level, drop down a bit lower and get some more wall length, so that you can build speed on flat ground. Then angle yourself in line with the slope of the wall, shoot up the wall, and get where you need to go.
This game is surprisingly resource-intensive, which can present a problem if you are playing with low battery life or with a crappy phone. If you need to save battery life, go to the options screen from the main menu. Then click off the little box that says Screen FX. This actually makes the graphics clearer, and it also saves battery life and stops lag if you have any lag.
There are actually two different characters in this game. One is Mother (the motherboard) and the other is a former virus (the pink character with the flower in her icon). The blue levels are where the story advances with Mother and the pink ones are where the story advances with the former virus. Both characters are protagonists, despite what Mother will try to have you believe early on in the game. You need to beat both of their sets of levels to advance in the story.
You can earn shiny gems as you go through the game, but the shiny gems don't actually buy you anything. In reality, they serve as both a driver of the story and as a parody of games where you earn currency that actually does buy you things. The pieces of data are more fun to earn, as they give you some of The User's writings and journal entries. Tap the little stars around the level to receive pieces of thought from Mother.