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We just played, and I won. Despite having seen his Mew use Softboiled, I still thought it had Explosion, so I used Ice Beam, thinking it was my only shot. This saved me the game.
I beat Giga Punch in a match full of misses (Thunderbolt included), Paralysis, FP, etc. on both sides. Now time for the follow-up victory. Should fight him again tomorrow I guess.