Watch her build carefully in order to counter her. Some Diana players would likely stack lots of attack speed such as Guinsoo's Rageblade, Nashor's Tooth & Wit's End in order to compensate Moonsilver Blade. If this happens, build Randuin's Omen against her.
Stay away from Diana if she uses Pale Cascade at it grants a shield.
Saving your channeling abilities like Death Lotus & Bullet Time after she missed Moonfall can cripple Diana.
Fiora is considered one of the best counters to Diana for a few reasons:
First, Fiora can disrupt Diana's combo with Riposte. It is even worse if Fiora parries moonfall for a potential stun on Diana in the process.
Second, Moonfall has a slightly higher cooldown than Riposte. Even building Cooldown Reduction items on Diana is not even enough whenever Fiora can also build Cooldown Reduction items.
And finally, Fiora can also outscale Diana by late game.