Nobody bothered to answer this part of the question yet. It's something I always wondered about when I was a nub, so when it finally came time to make my nib I felt like a virgin about to have sex for the first time.
What happens in the SQI arena? XD
1. 6 people get all their seals, pots, best gears, etc. together and meet in Yuno. For best results, you should have a bio and/or champ, an hp, and the rest is open to whatever you want.
2. Party up! Make sure everyone has all four seals.
3. Upon talking to the little man you'll be warped to a small room, where you wait until you're all ready to go.
4. When everything is ready, each person will enter a little chat box in the room and when all six are in the chat box, the party is warped to the arena.
5. MvP time! If it's your first time you'll likely not even know what's happening. Bio/champ do the majority of the damage, and the others just do whatever they can.
6. At the end, you'll be able to go to Valhalla. At this point you can make your SQI (if you were able to bring the ingredients), but no matter what
make sure you take to the big guy before taking the exit to the south. Otherwise you will have to do the entire arena over.
