Finish every single level in Sky Canvas mode, getting over 90 points to get Auto Gyro.
Get enough Acrobatic Points in Adventure Mode so that at least 10 of your mission rankings have circles, this will unlock Corsair.
Finish every single level in Target Mode with a gold rating to get the Golden UFO.
If you finish every level in Adventure Mode, the ME-262 should be available.
Beat Aventure Mode with a grade of A to get the Silver UFO.
If you finish Adventure mode with ten minutes or less, you will get the Stealth Fighter.