Significantly overpowered by the fact that she doesn't need mana or mana regen to spam two fairly significant nukes (both based on attack) with less than 10 second cooldowns, in addition to her best-in-game carry passive (roughly equivalent to Jax's ult). The only part of her that isn't straight up broken is the ult.

Imagine if you made Tristana's rocket jump and ult both have 10s cooldowns, made her ult bounce to 6 targets, made her attack speed skill passive, made her AoE-on-death use Exhaust as the active instead of the weak DoT, made them all free, and made them all instantly cool down if she got an assist or kill. THAT is Katarina.