This Seeking Tech guide will show you how to find The End’s Parrot in Metal Gear Solid 3: Snake Eater.
The bird is always located (at least in Normal Mode) on the rooftop of the small building in the west side of the starting area (Sokrovenno South).
To get there without getting spotted, go prone and then equip your best face and camouflage. You then need to crawl over to the small building.
Once you get close, shoot the bird down. Keep in mind that The End can still spot you if you try to get the downed bird. Just in this case, try to throw a smoke grenade first.
You can use the video guide below as a reference:
If you beat The End normally, then his death scene would play out differently depending on if you kept his parrot alive or not.