Almost any prayer can be helpful during anxiety attacks or depressive episodes. I find Eucharistic Adoration to be particularly calming and uplifting. Developing a regular practice of visiting Christ in the Blessed Sacrament will help to bring peace and joy.

The Rosary is a devotion I find particularly effective during an anxiety attack. Many times, I’ve woken up in the middle of the night with an anxiety attack that prevents me from going back to sleep. I have found that getting up and praying 5 or 10 decades of the rosary will calm me enough that I can get back to sleep.

The Blessed Virgin Mary understands anxiety and depression. Scripture tells us she was extremely anxious when Jesus was missing for three days. During the crucifixion and death of Jesus, her sorrow was tremendous. There is no fear or sorrow that our Mother can’t comprehend, and she wants to comfort us. Simply praying a Hail Mary apart from the rosary can be helpful.

Hail Mary, Full of Grace, The Lord is with thee.
Blessed art thou among women, and blessed is the fruit of thy womb, Jesus.
Holy Mary, Mother of God,  pray for us sinners now, and at the hour of our death. Amen.

The Miraculous Medal prayer is another great one:

O Mary conceived without sin, pray for us who have recourse to thee. 

The Memorare is another excellent prayer:

Remember, O most gracious Virgin Mary, that never was it known that anyone who fled to thy protection, implored thy help, or sought thine intercession was left unaided. Inspired by this confidence, I fly unto thee, O Virgin of virgins, my mother; to thee do I come, before thee I stand, sinful and sorrowful. O Mother of the Word Incarnate, despise not my petitions, but in thy mercy hear and answer me. Amen.

Praying and reflecting on the Hail Holy Queen prayer is especially helpful. It is a great reminder that our joy is not in this world but in the world to come.

Hail, holy Queen, Mother of mercy, our life, our sweetness and our hope. To thee do we cry, poor banished children of Eve. To thee do we send up our sighs, mourning and weeping in this valley of tears. Turn, then, most gracious advocate, thine eyes of mercy toward us, and after this, our exile, show unto us the blessed fruit of thy womb, Jesus. O clement, O loving, O sweet Virgin Mary. Pray for us, O holy Mother of God. That we may be made worthy of the promises of Christ.

Praying to St. Michael the Archangel is helpful. Some of our anxiety and depression can be caused or increased by the fallen angels that seek to torment us. St. Michael, as the captain of the host of the Lord, will defend us. It is easy to feel helpless during an anxiety attack or depressive episode, and it can be helpful call out to an angel to fight along our side. When Jesus was in agony in the garden, the Father sent an angel to aid him, and he will send angels to help us too.

St. Michael the Archangel, defend us in battle, be our protection against the wickedness and snares of the devil. May God rebuke him we humbly pray; and do thou, O Prince of the Heavenly host, by the power of God, cast into hell Satan and all the evil spirits who prowl about the world seeking the ruin of souls.
Amen.

We can call our guardian angel to help us.

Angel of God, my guardian dear, To whom God’s love commits me here, Ever this day, be at my side, To light and guard, Rule and guide. Amen.

Fr. Ripperger provides this binding prayer to use against any fallen angel that torments us in a specific way. Determine how you are being attacked and say this prayer against that. For example, this can be used against a spirit of anxiety or a spirit of despair. I recommend watching some of Fr. Rippergers talks on spiritual warfare to get a background on when a prayer like this can be used.  http://www.sensustraditionis.org/Binding.pdf

The Litany of Trust is a powerful prayer to help us trust in God. In anxiety and depression, trust and hope fade quickly. Strengthening our hope can make a tremendous difference. With hope, a burden like depression is much easier to carry. Without hope, it seems impossibly heavy.  https://sistersoflife.org/wp-content/uploads/2019/05/Mobile-Litany-of-Trust-English-1.pdf