No Encounter Equipment
Toward the end of the game after you gain control of the airship, there is so much you will probably want to do before you go defeat Sin. You will want to further fill in your characters' sphere grids, you will want to acquire their Celestial Weapons, you will want to find any remaining Al Bhed Primers, and you will probably want to do some side quests, like taking on the Dark Aeons. To make your life easier, I absolutely recommend acquiring a weapon or armor with No Encounter at this stage of the game. Acquiring Lulu's Celestial Weapon is dreadful and notorious, and is hard enough without fiends randomly popping up.
There are several ways to get No Encounter equipment. I'm going to discuss a few of those below.
The easiest and quickest way is to defeat Geosgaeno, the fiend Tidus encounters near the beginning of the game. You probably remember him. He's the giant sea creature who swam in and ate fiends Tidus was fighting before chasing Tidus into the temple he first met the Al Bhed in. When you gain control of the airship, you will be able to enter coordinates and find new places. If your put your cursor somewhere around (12,57), you will unlock Baaj Temple where you will be able to fight and kill Geosgaeno once and for all. It's not necessarily an easy battle, but if you've developed Tidus, Rikku, and Wakka throughout the game, you shouldn't have problems. When you defeat Geosgaeno, he will either drop a Reflect armor or a No Encounter weapon. The latter is what you want. It's a 50/50 drop, so if you receive the armor, I recommend restarting and fighting Geosgaeno again.
If you were anything like me in my last playthrough, you might have saved the game after defeating Geosgaeno without realizing that you received a No Reflect armor instead of a No Encounter weapon. It's okay; it happens to the best of us. I kicked myself for days after doing it, and even abandoned my game for months after, because it annoyed me so much. Acquiring No Encounter equipment seemed daunting and well, almost impossible to me for a long time. I tried several different things.
I read somewhere that you can attach No Encounter to armor if you have 30 Purifying Salts. I farmed and farmed for those damn salts from Fallen Monks in Zanarkand for weeks. It's a super rare steal. I ended up with 12 before I said, "screw this," and decided to try other things. You can earn 99 Purifying Salts from the Monster Arena by unlocking Fafnir. To do so, you have to capture 4 each of 5 different dragon species throughout Spira. The problem with that is the spawn rate for those dragons was so low, and I kept running into Dark Aeons I wasn't ready to fight. Screw that, too. I gave up on the Purifying Salts. If you can't tell, I can be impatient when I'm frustrated.
Finally, I decided to look for fiends that have a possibility to drop No Encounter armor. There are two that you have access to before Sin: Ghosts and Wraiths. The easiest for me to find were Ghosts. They are located in the Cavern of the Stolen Fayth, and are somewhat of a rare spawn there. When you enter the cavern, if you head right, you will find a small room that has a single treasure chest in it, and is illuminated green. I call it the Green Room. The whole room just glows green. It isn't said or supported anywhere, but it is in my experience that that room spawns more rare fiends than anywhere else in the Cavern. While waiting for Ghosts, I fought and captured ten of the very rare Tonberrys there. I recommend capturing Ghosts here because of their slow spawn rate, but how many you capture is up to you. I went ahead and captured 10 Ghosts here to complete them for the Monster Arena. Another reason you will want to capture them is because in addition to not appearing very often, killing Ghosts does not ensure a No Encounter armor drop. The drop is random, and you can kill dozens before acquiring one. The easiest thing to do is capture a Ghost, and then head to the Monster Arena, and fight them over and over again until you get a drop. To me, this, by far, was the simplest way to acquire the No Encounter armor after missing the weapon drop from Geosgaeno.
I was so happy with my find, and after being frustrated for so long about missing the weapon drop from Geosgaeno, I had to write this guide to help the poor, frustrated soul who made the same mistake I did. I hope someone finds this useful. If so, I will feel a bit better about the hours of my life I threw away farming Purifying Salts. No, no, I won't. I'm still bitter that those hours of my life are gone.