There is a CocoaPods that can to that: DoneHUD.
I didn't test it (first one found on CocoaControls), but it seems to do the job for your needs.
The main idea behind it:
UIView that you will display on (full) screen.
You can add a
UIVisualEffectView effect to it if available (iOS8+), or just use a color with some transparency (opacity < 1).
You can use
UIBezierPath to draw the path of the checkmark and use then
CABasicAnimation to animate the drawing effect on the layers.
UILabel as it subview at the bottom if you want to add text.
There are others results on CocoaControls if you want some inspiration on how to do an HUD (Head-up display).