1.Use her 2 before the fight quickly to fill it up and then use it at the end of the combo when it's filled up for maximum damage
2.Don't forget to buff allies and towers when possible (Default key on PC: Space)
3.You can use your ultimate to pull enemies into unfavorable positions, including your tower and fountain! It's very useful in Arena. If they're pushing towards your base just hop back in and pull them into your fountain for a funny kill.
4.You can actually build Hecate as a support or half-support. Keep an eye out for HP items.
5.Keep an eye out for low health teammates, your 3 can sometimes really save them in a pinch.
