71 dart /AC heater core removal

Yes, the whole box has to come out.
Obviously you have to take any under hood hoses off first.
Then unbolt the blower motor under the hood.
Take the J hook off the inside of the passenger side vent box door if it has one.
Start lowering the box down while disconnecting control cables and electrical connections.
Remove the clips that hold the two halves together.

From there it's pretty obvious what to do.

("Dogs breakfast" before or after he ate it?)
I am assuming you meant after. :D