Considering how the tension/mp bar works and how powerful crit/super crits are, not sure if any challenge runs would actually be "challenging".
Even using bad pilots(pilot stats have an effect, but even a terrible pilot in a halfway decent suit can be godly), or bad suits (so long as it doesn't die, getting into High Tension should allow it to ohko grunts and at most 2hko boss units.) won't make the game more challenging.
I suppose you could try only melee or something, though that's more of limiting options moreso than actually being challenging.
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Maaya Sakamoto and Younha are amazing~ <3 <3