Being immune to criticism isn’t really a component of Dumbiverse Amazi-Girl.  If anything, Amber probably worried she was too immune to some things, needing to be reined in.  Cross-continuity, Amber went on a journey from “worried she wasn’t standing up for herself enough” to “worried she was standing up for herself a little too much.”

However, “I am [superhero name] and I am [superpower]” is a mantra repeated by Nightguy, which also probably cribs a little from Batman and his ability to breathe in space.