In Mega Man X2, the secret boss encountered when X fails to collect all of Zero's parts is Zero. This rebuilt version of Zero appears midway through the Central Computer stage, where X must fight him before continuing toward Sigma.
The encounter changes according to the player's success in the X-Hunter subplot. The X-Hunters—Serges, Agile, and Violen—possess pieces of Zero's body. If X defeats them and recovers all three parts, the real Zero is restored and ultimately destroys a gray-armored Zero clone. If X misses any required part, the X-Hunters retain the components and Zero is rebuilt under Sigma's control.
The name X-Hunter is therefore a tempting but incorrect answer: the X-Hunters are the trio responsible for the plot, not the boss fought in this branch. Vile and Sigma are also important figures in the series, but neither is the alternate mid-stage opponent in this specific scenario.