You will get this achievement fairly easily through normal play. To unlock a lucky ticket, you need to earn enough "Lums" (points) in a level to earn the gold trophy. When you do, you also unlock a Lucky Ticket. Simply earn 10 gold trophies as you go along, and scratch the Lucky Tickets as they appear.
Remember, the number of skulls under a painting indicates the difficulty, with 1 being very easy, and 5 being insane. Choose easier levels for better chances at trophies. Again, normal play works fine. I earned this before I even finished all the levels in the "Teensies in Trouble" painting.
Happy Hunting!
- Dan