Amanda's really heavy, so she doesn't really gain altitude quickly enough. She's just too fat I:
Press up until you notice that the blades of the front rotor are just about to start intersecting with each other. Once you reach the desired height, tap down a few times to generate less lift. She should lean forward a little and stop going higher.
It really isn't hard to fly around with her once you get the hang of it. Use I, K, left and right to balance her out. You can always rebind the controls to your liking.
Flamethrowers are your main anti-infatry weapon. They're most effective on the 5th level, Queen's Fodder. Obviously don't activate them before they drop to the ground, that would basically be a death sentence for Amanda.
The driller is supposed to help you after you're out of ammunition, it also helps with killing sheep (since dragging the heavy aircraft around would take ages), destroying various buildings (like the towers in Duke's Plea) and cutting down crops (since, apparently, drills can do that). Hope I helped c: