You can win a lot at this game with just 5 steps:
Each time you shoot try to make the arrow line up with the bullseye.
Hold the space bar until the power is half way between a bar.
Release the space bar and watch the arrow fly into the bullseye.
Claim your bonus out of:
To win with your bonus do the same, except use less power for closer, and aim at the ring for fire.
And that is how to win at Ultimate bullseye! – lil_gem_gal