The easiest way I can see:
1) Make the skill shot (ie. hit the moving target) on your first ball. If you got the "lock is lit" award, the Skyscraper should be lit, and you're good. If not, restart the table and try again.
2) Use the middle ramp to lock the ball in the Skyscraper.
3) Get the ball in the mission hole and choose the Sniper mission. (This mission requires you to lock balls in the Oil Tanker.)
4) Use the right ramp to get the ball in the Oil Tanker and the achievement should unlock.
Losing balls during the process should be fine, you can get the skill shot on the first ball, lock it in the Skyscraper on the second ball, and the Tanker on the third. You can't lose a ball between steps 3 and 4, as losing a ball ends the mission; if you do, hit the mission hole again.
Thanks to Campotech for confirming that a single locked ball in the Skyscraper is enough, you do not need to have two in there (the wording on the achievement, prior to getting it, is a little ambiguous).
If you have clarifications, questions, or if there's a simpler way, please leave a comment!