Similar to Elder's Falz Arms, you'll need to battle Loser's guardian here over and over until 30 minutes up. Note the progress meter at the top of the screen.
In this particular instance it's using ice-based attacks. It can also attack you with lightning or fire. I've heard it is capable of switching in mid-battle but I've never seen it myself. Maybe that's only the rare variant? Speaking of which...
（C）SEGA
『PHANTASY STAR ONLINE 2』公式サイト
http://pso2.jp/