Is this possible to get this simple animation to output smoothly?

Can anyone help?

I want the illustration to fly in (quick animation preset) and then slowly move up and down in infinite loop.

The problem is both animations are starting at the same time and when “fly in” animation is finished the illustration jumps/jerks into position because the move animations has already started.

If you put a delay on the move animation then the illustration won’t jerk into position but the move animation will have that delay in every loop.

Scroll down to see the animation!

Any Ideas? I still can’t get it