Joachim is Khan's de facto second-in-command, and the only other member of his motley crew who has any dialogue. (Yeah. Khan loves him some movie villain monologuing.)
He's loyal to Khan unto death (his last words are "Yours… is… superior"), but he's less blinded by the need to cut Kirk open and do horrible things to his internal organs. That gives him the clarity to tell Khan things he really needs to hear…like the fact that maybe they're wasting everything they've gained in a pointless hunt for vengeance.
JOACHIM: We're all with you, sir, but consider this: we are free. We have a ship and the means to go where we will. We have escaped permanent exile on Ceti Alpha Five. You have proved your superior intellect, and defeated the plans of Admiral Kirk. You do not need to defeat him again.
He's even willing to push the point before the battle in the Nebula, to the point of telling Khan "no." (We're guessing "no" isn't something Khan hears a lot.)
JOACHIM: No sir! You have Genesis... you can have whatever you...
That serves an important purpose as far as demonstrating Khan's tragic flaw. Khan can't say he wasn't warned against his hellbent vengeance-fest.
Instead, Khan goes into it eyes wide open thanks to Joachim's question. He can't hide behind ignorance—especially because the advice he gets is from his loyal lieutenant, and he knows that it's delivered in his best interests.
But that's the thing about hellbent vengeance-fests: they're not too susceptible to reason.