From “Breslov Eikh She-hu: Breslov the Way It Is”
Customs and Practices, Past and Present
By Dovid Zeitlin and Dovid Sears (work-in-progress)
SHoVeViM (SHoVeViM-TaT in a Leap Year)
Breslover Chassidim used to fast until the late afternoon one day a week (usually on Thursdays) during the period of SHoVeViM – i.e., the weeks corresponding to the Torah readings of Shemos through Mishpatim. According to the kabbalists, this period is conducive for each person to make amends for his part in Adam's sin of separating from his wife after the exile from the Garden of Eden. In this spirit, some Breslover Chassidim in Eretz Yisrael today refrain from eating any davar min ha-chai (animal product) for a twenty-four hour period, or more commonly from dawn until nightfall, once each week during SHoVeViM.
(See Rabbi Levi Yitzchok Bender, Si'ach Sarfei Kodesh IV, 204)
Reb Noson mentions in Likutey Halakhos (source needed) that during the weeks SHoVeViM, one should cry out during selichos. (Many Ashkenazic congregations used to recite selichos during SHoVeViM. Although this is less common today, there are some who do so in Eretz Yisrael.)
However, Rabbi Levi Yitzchak Bender recalled that in Uman, the Breslover Chassidim did not recite selichos during ShoVeViM.
(Si’ach Sarfei Kodesh IV, 205)
Reb Avraham Sternhartz fasted the whole day during the weeks of SHoVeViM; however the details of when and how often are unknown.
(Heard from Rabbi Avraham Shimon Burshteyn, citing Rabbi Moshe Burshteyn)
In a letter to Rabbi Avraham Jacobovitch, Rabbi Shmuel Horowitz recommended fasting during SHoVeViM until noon one day a week, such as Thursday or Friday; and to refrain from any daver min ha-chai on two other days a week, such as Monday and Wednesday, as long as doing so would not hurt his health. He added that any such effort is good and helps, even if one can only fast for an hour or two in the morning, etc.
(Rabbi Shmuel Horowitz, Michtevey Shmuel [Jerusalem: Keren Rabbi Yisrael Dov Odesser, first edition], Letter 16, pp. 69-70)
As for the hanhagah of refraining from any davar min ha-chai, Reb Gedaliah held that this does not include such things as the small amount of egg white smeared on bread before it is baked, or even adding a little milk to coffee.
(Heard from Rabbi Avraham Shimon Burshteyn)
Reb Noson had an extra shi’ur of Tehillim that he said during the days of ShoVeViM.
(Rabbi Shmuel Horowitz, Michtevey Shmuel [Jerusalem: Keren Rabbi Yisrael Dov Odesser, first edition], Letter 16, p. 69; ibid. Letter 23, pp. 93-94. Reb Shmuel Horowitz understands Likutey Moharan II, 73, which discusses the recitation of Tehillim in connection with parshas Shemos, as also alluding to the recitation of Tehillim during the weeks of ShoVeViM.)