If something is done astonishingly, it is done in an incredible, amazing manner. It will blow your mind. Someone who gives away a million dollars is astonishingly generous.
To astonish is to amaze, and anything wild and surprising is astonishing. Add an -ly to the end to form astonishingly and that describes something done in a way that completely surprises. Great athletes play astonishingly well, a sunset that takes your breath away is astonishingly beautiful, and someone who suddenly leaps out of a deathbed has astonishingly been cured! This is a strong word for things you can hardly believe are happening.