Play the NOVICE version first to learn how to control the bird. Try keeping your flight even and steady, rather than bouncing off of ledges.
Stay away from the sides of the jousting arena, since a Buzzard Rider or Pterodactyl could appear unexpectedly.
Collect eggs quickly after they reach the ground. If you wait too long, they'll hatch into new Buzzard Riders.
Clear your screen of opponents as quickly as possible. The pterodactyl will appear if you wait too long.
Stay as high as possible on the screen, then drop down on your opponents.