From StrategyWiki, the free strategy guide and walkthrough wiki

After the arrival scene, follow Rikku and Paine along the path. You will come to a part where some has broken away and you must hold down O as you approach it to reach the other side. After you will need to Hold O again to climb up a small step.

You will reach another gap to jump across but if you just let Yuna fall down you can gain a Yellow ring from a chest there. Equip it on someone, possibly Rikku, then climb back up, and jump across.

After a short scene take the stairs down to a save sphere, then walk between Rikku and Paine to a switch on the wall and press it to activate the lift. After another short scene, walk down to what resembles an intersection. Go left and climb up the ledge to get an elixir from the chest. Go back to the intersection and climb up the right side.

Logos, Ormi and Leblanc are back. Use Power Break, Darkness Dance and Thunder to finish them off easily. If you have learnt any new skills by now, try them too.

A 6 minute timer will start, but as long as you don't panic, you can get all the items here with plenty of time to spare. Be sure to get them as you can never return here and once you reach a place where the timer stops, you can't turn back for anything you missed.

Run along the path and jump the small gap. Run to the end for a chest then go back a bit and cross a colapsed column to the left. From here, run to the door. At the first intersection along the path, climb up the left and right sides and press the switches on each side. Don't worry about the time limit, even if you only have 2 minutes left you should be able to do this and still make it.

Run forward and hold O to jump across the pillars that serve as stepping stones. Take the right turn and follow the path to a chest outside containing a Red Ring. Go back to the main path and continue straight this time. At the end of the path run along the path to a fallen column bridge near the end and at around halfway jump to the other side.

Go around the side of the tower to get a Star pendant then jump onto the ledge and go up to the spire. When you reach the Save sphere the timer stops, and up a bit is a chest containing a Muscle belt, for those who made it within the time limit. If you didn't, you should load and try again. It's not even hard and the Muscle belt is really worth it. Now, enter the hall and fight Boris.

Before the fight, put all the girls in the Warrior dressphere, and have them attack with Power Break and Flametongue. If you equipped the Red Ring, have the girl with it use Fire, While the other two use Flametongue and Power break. Every fourth turn he uses an attack called Sticky end. It can be very annoying, as it inflicts stop on your party, but just ignore it and the effects wear off. After the fight, go outside to board the Celsius. (next)