The Dynamic Hair title can not be challenged with the button or by talking to Dalair. Since it wasn't listed as an available quest like the other challenges, I just started the challenge on my own. I first changed the hair on my character, Inounoshishi, with a donor coupon. Then, I did the hairstyle quest, "Amoria: Beauty or Beast!", and used the coupon. After this, I purchased over 50 REG coupons – most from Midori in the hair salon, and some from the Cash Shop – and used them all. I have not been offered the title of "Dynamic Hair".
It just came to my mind. I remember when I hit lvl 200, I had to struggle to get the lvl200 medal because I already accepted too many quests from Dalair and he didn't allow me to take over a fixed number. Only after forfeiting few quests from him, I could obtain the quest for lvl 200 medal. Maaaaaaaaybe you are experiencing something similar and there is no room to accept that quest?
Yes you have to, and you are not even able to start the quest right now, that's why it still says "challenge" on your screenshot.
