Krypiakevych was born and raised in Lemberg (Lviv) in Austrian Galicia in a family of the Greek Catholic priest and emigrant from the Chełm Land.
In 1907 Krypiakevych on the notice of Andrzej Kazimierz Potocki, a Governor of the Kingdom of Galicia and Lodomeria, was imprisoned for student protests that took place near the Lviv University.
From 1911 to 1939, he taught at the Polish gymnasia (High Schools) at Zhovkva and Rohatyn and at the Academic Gymnasium in Lviv.
During the interwar period, Krypiakevych, being excluded from a university position by the Polish regime, continued to teach at various gymnasia and to actively support the Shevchenko Scientific Society.
Although he did turn away from Hrushevsky's populism to a pro-state interpretation of Ukrainian history, he revered his mentor's memory and in 1935 published a short biography of him.
The university was suppressed during the German occupation but Krypiakevych found work at the Ukrainian Publishing House in Lviv.
Unlike many of his Galician Ukrainian colleagues, mostly for family reasons, he decided to remain in Lviv after the German retreat westwards.
During the 1960s, he was very active at editing historical journals and mentoring younger Ukrainian historians, but a few years after his death in 1967, the Shelest Renaissance, which had briefly occurred under the protection of Ukrainian Communist Party leader, Petro Shelest, and had made possible so many of the cultural and academic achievements of the 1960s, came to an end (1972), and Krypiakevych's scholarly legacy was partly repressed.
Today, he is widely revered as one of Hrushevsky's foremost students, a continuator of his tradition, and one of the most important historians of western Ukraine.