No. Bizzaro can be a nuisance & antagonist but he can't be described as an "arch-enemy", certainly not in the same manner as Lex Luthor or Darkseid.
His arch enemy would be Lex Luther although there are many others. Most Notably are Bizarro, Brainiac, Doomsday, General Zod, and Gog.
Superman's main enemies include General Zod, Brainiac, Doomsday, Darkseid, and Bizarro.
Bizarro was created in 1958.
A bizarro is a strange person or a misfit.
Venom is Spiderman's archenemy.
Supermans tights are red.
The devil is the worst archenemy
Archenemy Record Company was created in 1997.
The Bizarro Jerry was created on 1996-10-03.
Mondo Bizarro was created on 1992-09-01.
Bizarro World - album - was created on 2011-02-28.
Carlos Eduardo Bizarro was born on 1979-01-09.