All the instructions will be same no matter the battery as long as you follow the memory stick part.
http://www.pspmod.com/forums/downloa...?do=file&id=22
There are the memory stick files, I'm not sure if they're for the SLIM however.
And P.S., you do not downgrade, you go straight from 3.80 to 3.71M33 because the slim cannot be downgraded (well pass 3.60 that is).