Picking up Daggers will significantly reduce Shunpo's cooldown.
Try waiting until the other team is distracted with fighting your team, and use Shunpo to teleport into the fray and unleash a devastating Death Lotus.
Using Shunpo on an allied Champion, Dagger, or minion can be a great escape tactic.
Katarina's abilities deal magic damage, so even if she's building Attack Damage items, get magic resistance to counter her.
Try to save a disable for when Katarina uses her Death Lotus.