I think "stand on my own two feet" is a very good translation. Depending on the context you could also say, "I can fly solo." This refers to a pilot's training. When someone first learns to fly a plane, an instructor must be present. After a certain amount of flying, the pilot is able to make a solo flight, or fly solo, without the instructor.
Other things that came to mind are working without a net (a reference to a trapeze artist who no longer fears falling) and removing the training wheels (a reference to a child who can ride a two-wheeler without help).