This Seeking Tech guide will show you how to find The End’s parrot in Metal Gear Solid Delta: Snake Eater.
The special bird is usually located on the left side of the starting area, at least in the normal difficulty mode. You should be able to spot it sitting on top of the small building.
If you need more help, you can check out the video below:
After defeating The End, the cutscene that plays afterward differs depending on whether his parrot is alive or not.