Reb Yechezkel Levinstein zt'l says that the primary tikkun, rectification, of our souls in shovavim comes from believing in Hashem. This is why the parshiyos we read during Shovavim discuss emunah, because that is how we attain atonement this time of year.
This lesson is also taught by Reb Meir'l Apte, zt'l, the Or LaShamayim (Bo). "In the early generations, the tikkun [of Shovavim] was with sigufim (fasts and afflictions), which remove the kelipos that cover over the neshamah and separate us from Hashem. But now, in the generation before Moshiach, the tikkun is easy. We don't need sigufim. The tikkun is with emunah, to believe in the Creator..."
It states (Yirmiyahu 5:1) ירושלם בחוצות שוטטו עשה יש אם איש תמצאו אם ברחובותיה ובקשו ודעו נא וראו לה ואסלח אמונה מבקש משפט, "Stroll in the streets of Yerushalayim and see now and know, and seek in its squares, whether you will find a man, whether there is one who performs justice and seeks emunah, and I will forgive her."
The Yesod HaAvadoh notes that it doesn't state that Hashem will forgive if He finds someone who has emunah. It is sufficient that He finds someone who is אמונה מבקש, seeking emunah.
Rebbe Tzaddok HaKohen (Tzidkas HaTzaddik 146) discusses the aveirah for which the Zohar states there is no teshuvah. Reb Tzaddok HaKohen says that emunah will bring atonement even for that aveirah. He writes, "The correction of this aveirah is to believe that nothing happens by chance. Everything is directed by Hashem's will. This is truly the main thing that is needed. There are 613 mitzvos, and they are all called עיטים, counsels, advice on how to attain emunah [that everything is by Hashem's hashgachah pratis."
Rebbe Tzaddok HaKohen explains that the aveirah that the Zohar is referring to is called קרי, and it states the punishment (Vayikra 26:28) קרי בחמת, "with a fury of happenstance. This is atoned for when one knows that there is no מקרה, and everything is directed by Hashem.
The Arizal teaches that during Shovavim, one must be extra cautious to say brachos over food with kavanah. (This counsel is quoted in Yesod v'Shoresh HaAvodah 12:2). Why is saying brachos over food an essential part of Shovavim?
One explanation, expressed by Reb Chaim Vital zt'l, is that the brachos remove the kelipos attached to the food, and then one can eat the food without getting attached to the kelipos that pull him down. But we can also explain that the brachos over the food help us remember Hashem, and that awareness is the taharah we attain during Shovavim.
