Born in Lavello, Basilicata, Tartaglia trained at the military school of Ceccolo Broglia and served the Republic of Florence.
On 26 June 1402, he fought in the Battle of Casalecchio; he was charged with overseeing the bridge of Reno, but he left his position to participate in the combat, leaving the camps without any defence on his side.
Released, he assumed responsibility for the defeat, but not enough to appease the wrath of Muzio Attendolo Sforza.
In 1409, he fought in the service of Ladislaus of Naples, defending Perugia and Civitavecchia from the assaults of Braccio da Montone and conquering Rome, scaring away the antipope John XXIII.
In 1418, he swore allegiance to Pope Martin V and occupied Assisi one year later and other territories between Lazio and Umbria.