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This is the Gandof Thunder Plains, a series of rocky fields constantly being bombarded by lightning strikes!

[edit] Dodging Lightning

Before you actually get onto the plains themselves, you'll be given a brief tutorial on dodging lightning strikes whilst crossing the Thunder Plains. There's not much to it — wait for the flash on-screen then press X to dodge it. You need to have relatively good reaction times, though. You can also get prizes, one of which is the currently unusable Venus Sigil for dodging 200 consecutive lightning strikes without leaving the screen, getting hit once or taking shelter underneath a lightning tower. This is more annoying and time-consuming than difficult, especially if you screw up once and get hit. It's not wise that you try this now because you'll be constantly entering random battles the whole time which makes judging lightning strikes more difficult (not to mention the amount of times you'll be struck with no warning just as you leave a battle).

Also, before you continue very far, it's a good idea to level up a bit. The monsters on Thunder Plains are a bit stronger than those you've fought before, so it'll give you an easier time. Tidus should have learned Delay Attack, and having him know Slow would be nice although that's a bit too much leveling for right now. Wakka should know Sleep Attack, and at the most Dark Buster or possibly Drain. Auron should know Magic Break. You may want to get Rikku up to knowing Luck (even though it's not that useful) since there's no intermittent skills between Steal/Use and Luck. Lulu should know the -ara elemental black magic spells, and at the most Reflex. You might want to get Yuna up to knowing Cura, but she should be a bit beyond Pray. At the very least your characters should know the latest skills mentioned by the time you leave Thunder Plains.

Kimahri's a jack-of-all-trades when it comes to the Sphere Grid, so you can choose pretty much which skills you want Kimahri to learn. Tidus', Wakka's, Lulu's and Rikku's main paths are the easiest to get Kimahri on, since their grid sections are blocked by just one Level 1 lock. Yuna's path forces you to backtrack a bit to learn everything, and Auron's is completely innacessible without going through a good proportion of either Tidus' or Wakka's paths first, and requires Level 2 locks which currently you can't open. Making him a Rikku or Wakka clone is probably the easiest for now. Otherwise, make sure you have him activate all of the centre section of the Sphere Grid that isn't blocked by locks (you don't have 3 Level 4 Key Spheres yet, so teaching Kimahri Ultima is impossible).

[edit] Crossing Thunder Plains

Before you even get to the Save Sphere there's a chest on the left which contains 2 Phoenix Downs. Past the Save Sphere on this side is another chest containing 2 Hi-Potions. Most of the enemies you'll encounter on Thunder Plains are obviously thunder-based, so weapons with Waterstrike will help out a lot. Here's a list:

• Melusines are lizards, so they're quick and agile, and have a higher rate of inflicting petrification and/or silence with their attacks compared to previously encountered lizards. Thankfully, Tidus still finds it easy to hit them, and one hit from him (especially with a weapon with Waterstrike, which the Brotherhood recently gained) will kill them.
• Kusariqqus are armoured dragons, and they have quite a painful physical attack (sometimes doing up to 900 damage, although around 450 usually). One hit from Auron will kill them, though, or two hits from Kimahri.
• Aerouges are flying mages. Their Thundara attack is particularly pathetic for it being an -ara spell, doing at most 300 damage. This is also their only attack, and they're vulnerable to Silence which renders them completely harmless. However, one hit from Wakka's ball kills them so inflicting Silence on them without killing them is difficult. You can Steal Lightning Marbles from these as well, which is better than the Electro Marbles you get from Larvae or Gold Elements.
• Buers are flying eyeballs. These are the same as the ones you encountered before, except they do a bit more damage. Their stare attack still inflicts confusion occasionally, and one hit from Wakka still kills them.
• Gold Elements are beefed-up versions of the Yellow Elements you encountered in Kilika Woods. One Watera from Lulu will kill them, but otherwise they have 1200 HP that is difficult to deplete quickly with physical attacks. They can't use Thundara but their Thunder attack does between 500-600 damage, so watch out (Yuna casting NulShock helps a lot).
• Larvae are new monsters. They have around 1500 HP, and use Thundara a lot for about 400 or so damage. They'll survive one Watera, and can heal themselves with Thundara, as well as bolstering their Magic. Don't let battles with these drag on too long or their Thundara will quickly be doing over 800 damage. One Watera followed up with one hit from Auron will kill them.
• Qactuars are Final Fantasy X's incarnation of an old favourite, the Cactuar. These won't hide in the ground or anything, but they still have stupidly high evasion, agility, defence and magic defence. Tidus and Wakka are pretty much the only ones who can hit them even half the time, for about 60-70 damage a hit. They'll attack for around 200 damage, use their infamous 1,000 Needles for 1000 damage, or use Run Away. It's not worth going all-out to beat them, but the reward is pretty good. They appear very rarely normally, although praying at the glowing Cactuar stones dotted around Thunder Plains seems to help them appear more often. Overdrives are definitely the best way to go here, and summon overdrives can quite easily overkill them.
• Iron Men only appear in the northern section of Thunder Plains. They have 3600 HP but they're armoured, so only Kimahri and Auron can hurt them a decent amount with physical attacks. They have no elemental weaknesses (Thunder does half damage), and only succumb to darkness often if hit with Dark Buster, which you might not have. Power Break is a good idea, since their physical hit can do 700-800, and Reaper can do 600-700 to everybody. Summons can take care of them pretty quickly, otherwise just keep Auron and Kimahri out to deal damage.

Head to the right-hand tower up ahead to speak with Maechen to learn a little more about Thunder Plains. Shelinda's also underneath a tower further on, where you can talk to her about Seymour and Yuna's supposed wedding. The side-area to the right near here contains a Water Ball in the chest and a cactuar stone you can pray to (using Square). Once you've got it, you can head all the way up to the next area, although before that, you'll get a creepy scene with Rikku acting weird. Turns out she's absolutely terrified of lightning. Make sure you actually rest at the branch and listen to Rikku, since it's got a Save Sphere and a place to buy stuff. Once you've talked with Rikku and everyone else, Rin will show up. After that, head into the room area for a few sequences with Yuna.

After resting, head on out, and you can now enter the northern section of Thunder Plains. You'll notice something on the ground just before the way to the next screen — this is a Yellow Shield (if it doesn't appear, go to the next screen then come back) for Tidus which has the rather handy Lightningproof ability, which makes all thunder-based attacks on Tidus do 0 damage. If you return to the previous screen after leaving, there's a chest which contains items dependent on how many lightning bolts you've dodged. You might get an Ether or something better if you dodged more.

Anyway, there's not much in the way of hidden or obscured chests in the next area of Thunder Plains, and you can spot the Save Sphere from here, so head towards it. Level up a bit more if you want. You'll have another sequence once you reach the large tower up ahead. Yuna will make her decision about her and Seymour, then you'll be on your way once more. On the right-hand side beyond this tower there is a chest containing 2000 Gil. Keep on going upwards — Thunder Plains' exit isn't that much further ahead, after which you'll be in Macalania Woods.