Retrieving apps and Music from 2 iCloud accounts to one iPhone
The apps are not « backed up » on account, they are at most link to an account.

Your only solution : 


If you still have your first password : Change your iTunes login in the iPhone and download the apps linked to that account. You'll get the cloud icon on the App Store if the app is linked, a price/free else.
You do the same thing with the second account. 


NB:  If you really forgot your password, you're going to need to rebuy the apps with your new account.