Man, their tutor had some good tips.
1. Say that Dongdaemun is great
2. Ask how much it is
3. Say it's too expensive
4. Ask for a discount
5. Compliment the seller's good looks (LOL)
6. Say how far you came to to come to Korea, and how expensive the plane ticket was
7. Say you won't come back and exchange it
8. Say you're paying in cash
9. Ask for just enough of a discount so you can still afford some street food afterwards
That really hits all the bases. I usually played the "I'm a poor student who came all the way to Korea to learn Korean because I love Korea so much" angle when I haggled at Dongdaemun or Yongsan.
I think they could have been more convincing, and the guy only gave in because of the camera there. I do admire their confidence in trying their hand at haggling, though. Hopefully with practice they'll become pros
.