For this mission, you have to enter the arbalest zone 10 times. The arbalest zone is located in the middle upper right, between the bicycle and your upper right flipper. To enter it, you have to light up the two lights underneath your upper right flipper first, by hitting them. Then you have to shoot the ball in between those two lights. Now the ball will enter the arbalest zone. There is a minigame, in which you have to light up all 4 lights on the ceiling, and the shoot the ball in the hole that opens. I'm not sure whether you also have to complete this minigame for this achievement or not, but try to complete it as well just in case. This achievement is cumulative across multiple games. Keep in mind you have to exit the game with the back button and not with the home button. Leaving the game with the home button will not save your progress. To have a visual guide for this achievement, look at this youtube video made by Zathras. This guide is for all missions in Da Vinci Pinball. The Arbalest zone mission can be found starting from 1:30.