I have never studied the details of the war on the Ukrainian front, but I will try to look for something in Russian sources. I do not promise to do it quickly - I have little free time now.
https://en.wikipedia.org/wiki/Proskuriv_offensiveFrom the Russian Wikipedia:
Proskurovskaya Operation (1919)
The Proskurovskaya Operation or Proskurovskaya Breakthrough was a successful military operation of the UPR army, conducted in June 1919 against the Red Army troops and allowing the expansion of the territory controlled by the authorities of the Directory of the Ukrainian People's Republic.
Military-strategic situation
In early April 1919, the UPR army, under pressure from the Red Army, was constantly retreating to the west and at the end of May, one part of it crossed into Romania, while the other crossed the Zbruch River and found itself on the territory of the West Ukrainian People's Republic. At that time, the ZUNR was at war with Poland. By May 28, the UPR government and army controlled only one Kremenets district of Volyn, and the ZUNR government and troops controlled only the eastern districts of Galicia.
Operation plan
In May 1919, the command of the UPR army formed 11 new divisions with a total of about 12 thousand people with 64 guns[1]. Thanks to this, in the last days of May, the deputy chief of the General Staff of the UPR Army, V.N. Tyutyunnik, head of the operational department, developed a plan to break through the Soviet front in the direction of Proskurov (now Khmelnitsky). The main striking force was the Zaporizhzhya group of the UPR army, which was to advance from the Pochaev region to Teofipol-Starokostiantyniv and Volochysk-Proskurov. Separate detachments (corrals) of the UPR army under the command of commanders Udovychenko, Vishnevsky, Shandruk and others were to cross the Zbruch from the territory of Galicia and launch an offensive on Kamenets-Podolsky. The Sich Riflemen and the Volyn group covered the attackers on the northern flank in the Yampol-Teofipol region from possible attacks by the Poles and the Reds.
The UPR army was opposed by the troops of the 12th Army of the Red Army: in the north, in the Shepetovka-Rovno area, the 44th rifle division (8,000-9,000 bayonets with 24 guns), in the Volochysk-Proskurov area, the Separate and International Brigades (about 5,000 bayonets with 18 guns), in the south, in the Kamenets-Podolsky area, the Separate Bessarabian Brigade (about 3,000-3,500 bayonets with 12 guns and 2 armored trains).
Progress of the operation
On June 1, 1919, the Ukrainian army began a general offensive. Already on June 3, 1919, the UPR troops occupied Volochysk, Cherny Ostrov and Kamenets-Podolsky. On June 5-6, the 1st Hutsul Marine Regiment captured Felshtyn (now the village of Gvardeyskoye) and Yarmolintsy.
On June 6, after a fierce battle that lasted from 5 to 8 am, Proskurov was captured. Nikolai Kapustyansky, an employee of the General Staff of the UPR Army, wrote: “On June 6, Colonel Vladimir Salsky[2] led a decisive offensive on Proskurov with two divisions: the 6th from Cherny Ostrov, the 8th from the northeast. The 6th Division boldly attacks Proskurov and captures it after a heated battle. The Bolsheviks stubbornly defended themselves, with great support from 3 armored trains that staunchly fought our artillery. The importunity and energy of the 6th Division, as well as the threat to Proskurov from the 8th Division, decided the matter. Much booty falls into our hands… The Bolsheviks retreat to Zhmerynka. Our armored train followed them to the Derazhnya station"[3].
On the same day, the Sich Riflemen drove the Red Army out of Starokostiantyniv. In mid-June, the Zaporozhian divisions occupied Derazhnya and Novaya Ushitsa.
Results
The main strategic success of the Proskuriv breakthrough was the capture of Kamenets-Podolsky, Derazhnya, and Novaya Ushitsa. After capturing this line, the Starokostiantyniv-Proskuriv-Kamenets-Podolsky, as well as Volochysk-Proskuriv-Derazhnya railways came under the control of the UPR troops. This gave the UPR Army command the opportunity to transfer parts of its base (everything that was in trains on the Ternopil-Pidvolochysk line), as well as rear institutions through Proskuriv to Kamenets-Podolsky. The success allowed the Directory and the UPR government to settle in Kamenets-Podolsky for a long time.
Thanks to the victory, the Ukrainian army continued its offensive in the second half of June and early July 1919 and managed to occupy Zhmerynka and Mogilev-Podolsky on July 4.
https://ru.wikipedia.org/wiki/?????????????_????????_(1919)
The Russian version of the page has a photo of the Sich Riflemen in 1918.
One interesting thing is the participation of the Ukrainian Marines in the battles.


Officer and sailor of the Ukrainian 1st Hutsul Marine Regiment

Ukrainian artillery battery in battle near Proskurov.