I've observed that sometimes I just have to make two kills in order to dominate a certain player, sometimes thrice or is there any other factor that matters?
This will be helpful to unlock certain achievements that depend on dominations.
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Sign up to join this communityYou have to get any combination of four kills or assists on an opponent in a row (that is, without them getting either a kill or an assist on you) to dominate an opponent.
Once dominated, either a single kill or assist is enough to get revenge.
Check the TF2 wiki for more info on dominations.