The full explanation of the Rosa Mystica devotion is on this website.
See also The Divine Mercy Novena here

The devotion does not seem to specify exactly which prayers are said, so below is my suggestion. You can substitute whatever is, in your good judgment, the best prayers, sacrifices, and penances to do on these days.

I suggest, daily, praying some or all of the following prayers, in any order:

Golden Arrow Prayer
May the most holy, most sacred,
most adorable, most mysterious,
and unutterable Name of God
be always praised, blessed,
loved, adored and glorified,
in heaven, on earth and under the earth,
by all the creatures of God,
and by the Sacred Heart of Our Lord Jesus Christ
in the most holy Sacrament of the altar.

True Holy Eucharist Prayer
May the most Sacred Heart of Jesus
be adored and loved
in the true Holy Eucharist
at every Mass
throughout the world
until the end of time.

May the most Sacred Heart of Jesus
be adored and loved
in the true Holy Eucharist
in every tabernacle
throughout the world
until the end of time.

May the most Sacred Heart of Jesus
be adored and loved
in the true Holy Eucharist
by the heart of every Christian
throughout the world
until the end of time.

Anima Christi
Soul of Christ, sanctify me.
Body of Christ, save me.
Blood of Christ, inebriate me.
Water from the side of Christ, wash me.
Passion of Christ, strengthen me.
O Good Jesus, hear me.
Within Thy wounds hide me.
Suffer me not to be separated from Thee.
From the malignant enemy, defend me.
At the hour of my death, call me
and bid me come to Thee
That with Thy Saints I may praise Thee
Forever and ever. Amen.

Rosa Mystica Prayer
Blessed Virgin Mary,
Rosa Mystica,
Most Pure Rose of the Most Sacred Mysteries,
obtain the Mercy of God for us
through the Sacred Heart of Jesus
and grant us repentance, conversion, and healing
through your Motherly Immaculate Heart.
Amen.

The Prayer of Praise to Saint Joseph

Rosary
[at least one decade]

Divine Mercy Chaplet
[at least one decade]

Prayer of the Publican:
O God, be merciful to me, a sinner.
[O God, be merciful to us, poor sinners.]

Seven Words Prayer
Jesus, Mary, I love you, Save souls

The Prayer for Healing

.

Pray some or all of above prayers daily for the first 12 days of each month. Please keep in mind the intention of the grace of chastity and purity for clerics, religious, and the laity — married as well as single.

On the 13th day of the month, pray extemporaneously (speak to God and Mary from your heart, in whatever words you may choose) and ask God for whatever favor you may desire. Celebrate the 13th day as a day dedicated to the Blessed Virgin Mary.

Mary: “I wish the 13th of each month to be celebrated as the day of Mary. On the twelve preceding days, special prayers of preparation should be said.”

Remember to pray also for the intentions of the Roman Pontiff. If you disdain or reject the Roman Pontiff, whosoever he may be, may God punish you. Those who have true faith believe that each and every Roman Pontiff will never err gravely, never fail in faith, and never lead us astray.

Alternately, the above prayers can be used as a Novena at any time, for nine consecutive days, for any holy intention.

[This particular form of the Rosa Mystica devotion
and the Rosa Mystica Prayer itself was composed by Ronald L. Conte Jr.]

“Penance means to accept every day all the little crosses and the duties too, in the spirit of penance.”

Our Lady finished Her dialogue with the words: “Live out of love!”

The seer, Pierina, interpreted the words Rosa Mystica as: “Mary is the master teacher of the innermost mystical life and the Mother of the mystical body of Christ….”

December 8th hour of grace

The Blessed Virgin Mary: “I come here to Montichiari because it is my wish to be appealed to and venerated as ‘Rosa Mystica.’ I wish people to celebrate each year on December 8th at noon the hour of grace for the whole world. With this exercise, one will receive numerous spiritual and bodily graces. Our Lord, my Divine Son Jesus, will be abundantly merciful so long as good men go on praying for their fellow men. As soon as possible, let the Supreme Shepherd of the Church, Pope Pius XII, know it is my wish that this hour of grace be publicized and spread throughout the whole world. If someone cannot go to church at this time, he is to pray at noon at home, and he will receive graces from me. He who prays on these bricks and sheds tears of repentance will find a secure ladder to Heaven and get protection and graces from my Motherly Heart.”

Detailed instructions for the Hour of Grace here.

Other Prayers:

Soul of Christ, sanctify me
Body of Christ, save me
Blood of Christ, inebriate me
Water from the side of Christ, wash me
Passion of Christ, strengthen me
O Good Jesus, hear me
Within Thy wounds, hide me
Suffer me not to be separated from thee
From the malignant enemy, defend me
In the hour of my death, call me
And bid me come to Thee
That with Thy Saints, I may praise thee
Forever and ever
Amen