Does Paragon require that the AFII it's equipped on to have fired at the target, or just some ship in the player's fleet to have fired on the target in order to proc the effect?

"You" in a ship upgrade card or ship ability refers to the ship.

Thanks for the clarification.

Gunnery teams says you can't target the says ship twice, so you have to get two firing arks on your target to use Paragon?

Correct.

The only way it happens is if you Double-Arc, OR, be second Player with the Advanced Gunnery Objective and have selected Paragon as your Objective Ship.

And you will only get the bonus die on the second shot.

Correct.

The only way it happens is if you Double-Arc, OR, be second Player with the Advanced Gunnery Objective and have selected Paragon as your Objective Ship.

And you will only get the bonus die on the second shot.