You can remove the A/C heater box without pulling the dash.
It can be an all day job to swap the heater core so be prepared in advance and set aside enough time to complete it, or spread it out over the weekend if this is your daily driver.
Be very careful disconnecting the A/C lines at the firewall. Sometimes these connectors are tough to separate without twisting and ruining the soft copper tubes that go into the car and of course remove the heater hoses.
The nuts that hold the heater box to the firewall are accessible in the engine bay, clean the threads very good and soak these with WD-40, pb blaster, liquid wrench or whatever. You want them to come off easily, if not, re-clean the threads and re-soak, if the stud starts twisting with the nut, it will break off the heater box inside the car and you don't want this to happen.
Inside the car remove the glove box liner to get to the vacuum lines and the heater cables, and also disconnect and then remove the ductwork that goes to the dash vents, and finally the bracket that holds the box up (just loosen the nuts that hold this bracket and leave it in place until you are ready to lower the box down).
You kind of have to pull the heater box back away from the firewall to clear the a/c fittings and then kind of twist and slide the box down from under the dash. I also remove the lower dash bolt behind the passenger kick panel and carefully pull the bottom of the dash out to get some more room for the box to come down and out from under the dash.
Once the A/C-heater box is out of the car you can remove the screws and clips that hold it together and access the heater core inside. This is a good time to clean all of the leaves and debris out of the box and I recommend a gasket/seal kit before buttoning it back up and reinstalling in the car.
I'm probably forgetting something, but that covers most of what I remember. There might be a J-bolt up inside the box where it attaches to the bottom of the cowl, I think you slide the fresh air door open to reach it, but that might be on a-bodies and earlier b's.
You really should get a factory service manual, if this is your first time or if you don't have a parts car to practice on. Maybe someone can post some pictures from their manual.
