The same way you beat any game in the 1980s and early '90s: lots of pattern memorization based on trial and error. In the arcade, that means lots of quarters.
Once a game like Dragon's Lair was memorized, you could play through the entire thing on only a couple quarters, to the astonishment of arcade bystanders.
Kids and teenagers had more time back then because smart phones and Instagram and YouTube didn't exist. People underestimate what a huge time sink those can be.
No one had Internet access. You could play a game, play an instrument, read a book, go to the mall and the arcade and maybe catch a movie, go outside, or watch whatever happened to be on the 3-4 network TV channels (or possibly cable if your family had the money). And TV back then was mostly terrible.
So if you had $10 in your pocket, that was an entire afternoon of entertainment at the arcade and movie theater.