After leaving the Cloister of Trials, you’ll basically be sent running from the area. On the road just outside the Temple, you’ll be running from a few Guado Guardians; if they reach you, you fight them. They’re little different than when they were with Seymour, so no real problems there. In any case, outside, continue across the large crevasse, picking up the Lv. 1 Key Sphere as you go. Once you reach Lake Macalania, there will be another scene with a boss to boot.
BOSS - Wendigo
Again, the Guardians tend to be supportive units in this fight to aid the Wendigo. They tend to use Protect and Shell on him to halve physical and magical damage, respectively. They also will Berserk it to buff his Strength, and can reinstill if it you get him out of it. Otherwise, they will use Auto-Potion for 1,000 HP healing on themselves and Thundara, Fira, and Blizzara to attack you. The Wendigo is much simpler, hitting with only basic physicals - however, once his HP falls under 50%, it will counter every attack with an attack that is 25% stronger than normal. It can also use a physical during this time that is 50% stronger than normal. That’s nasty when you factor in the Berserk and 40 Strength, easily 1,500~2,500 damage.
So, how to start? Firstly, the Wendigo is NOT your priority. I recommend sending in Rikku as early as possible. You can do this by keeping her out of the initial party; then have Tidus come in with the Sonic Steel (First Strike) equipped and swap to Rikku. She ought to get the lead on one of the Guados; she can then steal from him to stop his healing, then the same with the other later. Meanwhile, have Tidus get sent back in for Hastega while Lulu or Auron or whoever’s strongest begins to decimate the Guado Guardian. Once Rikku’s done, switch her out for Lulu or another Black Magic user so she can shatter the other Guardian, and have Tidus go on the offensive after the Hastega. Hopefully, the Guardians got in minimal buffing on Wendigo before their deaths. Then again, they can cast Protect or Shell when they die.
With that out of the way, we can now get rid of Berserk in some fashion, and preferably Protect and Shell. Berserk can be removed by using a Remedy or Esuna on the best. Protect and Shell can be a bit more difficult without Dispel on hand; if you do, though, great. Otherwise, you’ll have to have Yuna Summon Ixion and use Aerospark ; that has a Dispel effect added to it.
So, now, all of the boss’s buffs are gone, with no possibility of them coming back without extreme stupidity on your part. Weaken it further! This beast is still strong at 40 Strength, so why risk it? Use Power Break and Dark Attack/Buster on it; Power Break halves the Strength (to 20), and Darkness makes sure you are unlikely to be hit at all. (Darkness may take a few tries, as it is resisted.) If you want, throw in Armor and/or Mental Breaks to help your own offense.
The end result? Halved Strength, halved Defense, halved Magic Defense, and Blindness: its Strength is pitiful now, and that’s assuming it hits. It’s basically a quivering wimp. From there on out, it’s pretty simple. Keep a healer on-hand to Cure whenever it’s really needed, somehow, while you have two other offensive units do the work. When the boss raises his fists (under 9,000 HP), go for a more magical offense to avoid having to deal with counterattacks. (Note that if you get Sleep Attack/Sleep Buster to take effect here, Magic will not awaken the boss, and the Sleep lasts 20 turns, so you can work that in your favor as well.)
After the fight, you’ll end up inside Sin after he attacks. Speak with Rikku, then go to Kimahri. Open the chest next to him for a Lv. 2 Key Sphere, speak with him, then go north and speak with Auron. Open the chest you saw in the cutscene for an Avenger (it’s hard to see outside of the scene, though). Then go south to continue.