Problem with unique bird mobs

Well I was exploring a world. Looking for the unique mobs on it to hopefully get a gun drop. I saw a unique flying mob.. for like 2 seconds before it flew off screen never to be seen again. I've noticed that flying mobs tend to continuously fly upwards ever so slightly and at different angles. I have no idea what would happen to it when it hits the top of the world .. it was flying up at a pretty steep angle and it got away before I could get its attention.