I think there are elements of "resilience" with Epicurean philosophy, but yet in the modern psychology it seems that people use resilience as a way to put up with all the nonsense of unnecessary desires (such as desires for fame and status, etc.).
From the Letter to Menoeceus (Saint-Andre translation):
QuoteThird, keep in mind that some desires are natural whereas others are groundless [note]; that among the natural desires some are natural and necessary whereas others are merely natural; and that among the necessary desires some are necessary for happiness, some for physical health [note], and some for life itself. The steady contemplation of these facts enables you to understand everything that you accept or reject in terms of the health of the body and the serenity of the soul — since that is the goal of a completely happy life.
I would understand "serenity of the soul" as being the same as a healthy mind (a mind not filled with fear or anxiety), and within this healthy mind arises a feeling of ataraxia. So ataraxia is not something you do, but it is a feeling which is a result of wise living.