Hector's most famous kill is Patroclus, the second-in-command of Achilles over the Myrmidon forces on the Greek side of the Trojan War. Because of how close Patroclus was to Achilles, to whom he was related and had known since they were young, this led inevitably to Hector's death by the hand of Achilles, who was sore with vengefulness over his friend's demise.
The Wikipedia article "List of Trojan War Characters" has comprehensive tables listing the Greek and Trojan casualties from the war and who was responsible for each one.
Carlos Parada's website the Greek Mythology Link (GML) has two separate pages with dictionary articles listing Achaeans named in ancient sources dealing with the Trojan War, and the Achaean Leaders to whom they were subordinates. On the Trojan side, Hector does indeed have the highest kill-count.
Both of the aforementioned websites supply twenty-nine names of men killed by Hector, with Patroclus and Protesilaus of course being among them. Both websites provide fairly uniform information, although more detail is available on the GML entries than on the Wikipedia page, the latter of which is just bare tables of lists.
The main primary source for these entries that you'll find at the GML is Homer's Iliad, with references of where in the poem the information is drawn from. Certain characters have alternate endings based on variant accounts, however, and you can find the details thereof at the GML. Otherwise, to see simply the different versions as a plain breakdown, consult the lists on Wikipedia.
Protesilaus, for example, was otherwise slain by "Aeneas, Euphorbas, Achates or Cycnus" while Antilochus, if he wasn't killed by Hector, died at the hand of Memnon. If we subtract those two alternates, then Hector's kill-count is down to twenty-seven. The war-god Ares also helps Hector to kill Oenomaus, Oresbius, Orestes, Teuthras and Trechus.
For the sake of comparison with the other Trojans you have named, Polydamas's count is five (one of whom, namely the Boeotian Prothoenor, was a leader); Deiphobus has five (including one leader, Ascalaphus); Helenus is said to have slain only one man, a Pylian named Deipyrus; and Paris kills eleven soldiers, the only leader among them being, incidentally, Achilles.
The Iliad frequently makes reference to "mighty Hector" (e.g. in Book 10, twice in Book 11, & twice in Book 14) just as Achilles' son Pyrrhus himself does in Seneca's Troades 322. In Iliad 12, Hector is "the mighty deviser of rout" of whom the Greeks are terrified, and who fights the Achaeans furiously "like a whirlwind." He is also repeatedly called "godlike" and the "peer of Ares," although none of these might be saying much as regards comparison, since so many other fighters are tagged with these epithets of "mighty," "godlike," and "peer of Ares." Even Hector's old father King Priam is "godlike" in Iliad 24.
