I control a battlefield. My opponent attacks the battlefield. He has enough might to kill all of my units. However, when the units die, their deathknell triggers allow me to do damage and due to this, I am able to kill all of his attacking units. Does he still conquer?

No, the opponent does not conquer the battlefield in this scenario.

According to Rule 461.3.d, if both players have no units remaining at the battlefield during the "Determine Combat Result" step of the combat resolution (or if both have units remaining), the result of the combat is "No Result."

Because the result is "No Result" and there are no units remaining for either player at the battlefield, the battlefield becomes uncontrolled (per Rule 461.5.b). Since the opponent does not establish control of the battlefield, they do not trigger a Conquer (Rule 464.1).

The Sequence of Resolution:

1. Combat Damage Step: All units (both your defenders and your opponent's attackers) are killed.
2. Combat Cleanup: Your units' Deathknell triggers resolve (assuming they were added to the chain during the kill instruction).
3. Determine Combat Result: The game checks the battlefield. Since neither player has units present, the result is "No Result" (Rule 461.3.d).
4. Finalize: Because no units remain for either player, the battlefield becomes uncontrolled (Rule 461.5.b). Because no one established control, no Conquer occurs.