My attempt (names already known, specific dates looked up on Wikipedia):

1. Kushim (c. 3400/3000 BC)

2. Iry-Hor (c. 3170 BC)

3. Narmer/Menes (c. 3100 BC)

4. Gilgamesh (c. 2900/2700 BC)

5. Imhotep (c. 2700/2600 BC)

6. Djoser (c. 2687/2667 – 2668/2648 BC)

7. Khufu/Cheops (c. 2589 – c. 2566 BC)

8. Lugal-Zage-Si (c. 2358 – c. 2334 BC)

9. Sargon of Akkad (c. 2334 – c. 2279 BC)

10. Sobekneferu/Neferusobek (c. 1805/1760 – 1802/1755)

11. Hammurabi (c. 1792 – c. 1750 BC)

12. Ea-nasir (c. 1750 BC)

13. Nanni (c. 1750 BC)

14. Zoroaster/Zarathustra (c. 1700/550 BC)

15. Hatshepsut (1505 – 1458 BC)

16. Thutmose III the Great (c. 1479 – 1425 BC)

17. Nefertiti (c. 1370 – 1330 BC)

18. Akhenaten (c. 1353/1351 – 1336/1334 BC)

19. Tutankhamun (c. 1341 BC – 1323 BC)

20. Ramesses/Ozymandias II the Great (c. 1303 – 1213 BC)

21. Tapputi (c. 1200 BC)

22. David (c. 1000/800 BC)

23. Solomon (c. 1000/800 BC)

24. Homer (c. 800/700 BC)

25. Ashurbanipal (c. 685 – 631 BC)

26. Solon (c. 630 – c. 560 BC)

27. Draco (c. 625/600 BC)

@TheAllMemeingEye Additional figures I know the names of but that don't quite have sufficient evidence of historicity:

1. Osiris (c. 5500/3100 BC)

2. Enkidu (c. 2900/2700 BC)

3. Shamhat (c. 2900/2700 BC)

4. Moses (c. 1300/1200 BC)

5. Achilles (c. 1300/1100 BC)

6. Hector (c. 1300/1100 BC)

7. Odysseus/Ulysses (c. 1300/1100 BC)

8. Saul (c. 1030 BC – 1010 BC)

9. Rehoboam (c. 972 – 913 BC)

10. Romulus (c. 753 BC)

11. Remus (c. 753 BC)