KURAKHOVE, Ukraine—The Ukrainian 68th Jaeger Brigade spent the past year defending trenches in the country’s east against Russian onslaughts. Last week, they went on the attack. On Saturday, three platoons from the 68th took the village of Blahodatne from a larger Russian infantry force after a methodical firefight. Men from the Jaeger, used to fighting in fields and hills, said they had trained themselves in house-to-house combat and described using their American-made armored vehicles to blast open a Russian strongpoint. The last Russian defenders ran away through their own minefield. Few made it. Four of the Jaegers were killed taking...