kado,
from information i have, Access bank do not shortlist 2.2 for their apt test but am not rulling out the fact that their are 2.2 graduates working in access bank, but i can confirm to you that i have friends that graduated with 2.2 working in Zenith, GTB, UBA, First Bank, Diamond Bank, Intercontinental, Oceanic, Bank PHB, Eco bank, est infact even 3rd class (confidential). The main thing is for you to pass the aptitude test nad go in for Interview.
Cheers.