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So via the power of hacking a +8 priority 100% accuracy OHKO move into the game to beat everything, IRC managed to figure out how the Battle Tower equivalent works and all the rewards.
Opponents have set teams that stay the same each time you face them and are classified by tier; Tier 0 are complete idiots with no EVs and possibly even unevolved puppets, Tier 1 is less stupid but still don't know how to use EVs, and then the others are actually competent. You appear to go up a tier every 10 wins in a row, but that's not confirmed yet. Character power level seems to have some effect on their tier, but it isn't by any means set in stone. Suika for instance is only Tier 1, while Letty is Tier 4. Raiko's tier 2.
Set fights against certain opponents at 10, 15, 20, 25, 30, 35, 40, 45, 48, 49, and 50, all others are random. No repeats. Breaks are allowed every 5 wins.
Every 10 wins you get a reward: Rather than BP or an equivalent like in Pokemon, it's just items.
10 wins is 20 magical fragments.
20 wins is 5 prismatic candies.
30 wins is a new held item (Hakurei Amulet, which is in effect a second Native Grace)
40 wins are some fate threads.
50 wins gets you the upgraded version of the dream fragment discussed earlier in the thread.
Note that unlike in Pokemon, it is NOT infinite in length until you lose: Your streak automatically ends after 50 wins in a row (although you can run it again obviously); no trying to make a streak last 500+ wins in a row like some Smogonites do in this game.
Difficulty is a joke up until round 20, then it becomes legit Battle Tower levels of pain.
Fun fact: there was actually a hard counter to the hacked OHKO move in there, and it wasn't something with a "can't be OHKO'd" ability (since those only make it so you survive with 1 HP if you get hit by a OHKO move rather than flat immunity like in Pokemon).