Last name Achilla, Achille, Achilleo, Achillini, Chiletti, Chiloni, Chilesotti
Achille, Achilleo, Achilla, Achilli, Achillini, Dacchille, D'acchille, Dachille, D'achille
are patronymic, that is, derived from the father's name, in this case Achille = Achilles: name of Greek origin meaning "dark".
The patronymic could derive from the cult of St. Nereus and St. Achilleus, two Roman soldiers who converted to Christianity and were killed in Rome, probably in the persecution of Diocletian, and are revered as holy martyrs by the Catholic Church.
Also, it could have its origin in Greek mythology, Achilles was the main hero of the Trojan War and the strongest, fastest and most beautiful warrior of Homer's Iliad. Son of Peleus, king of the Myrmidons in Ftia, and Thetis, a sea nymph, Achilles was considered invincible, but not immortal.
Chiletti, Chilesotti, Chillon, Chilloni, Chiloni
They could also be derived from Achille, such as the name Michele = Michael.