Sawzall. With the master water valve turned off. A leaking pipe is a major rip out. No need to be delicate. The whole thing will likely need to be redone and you'll be lucky if it doesn't extend into other rooms of the home. The lathe will most likely be rotten, as well as some of the studs and sill.

Either a sawzall or just a keyhole saw.

With a sawzall you can start a hole without drilling, with a keyhole saw you drill a hole and then start from there.

Sawzalls can be rented, but count on buying your own blades.

Plaster and nail cutting wood blades are normally used for opening plaster walls.
The plaster will ruin the edge very quickly, so buy extras.

The blades at the rental place are likely to be limited and overpriced.

Even the big box stores have blades though.

Heck, a hammer will get rid of the plaster and let you in to the wall. The damage is likely to be pretty extensive. Yes, you will need to redo the whole shower. Plaster isn't waterproof and any tile wall on top of it in a shower will have mold behind it at a minimum. At a maximum, you only have that thin veneer over completely rotten mush. Water leaks quickly destroy homes so don't let it go on any further without taking action.

"Heck, a hammer will get rid of the plaster and let you in to the wall."

And liable to do damage to areas of plaster not damaged by the leak.

Hammers and plaster are NOT a good combination.

Thanks for the responses...

Someone also suggested that I fix the leak from the outside of the house (remove the siding, etc)... I guess no matter how I do this it won't be pretty...

Patching plaster is not as hard as it may first appear.

You can use blueboard (a tye of gypsum board) as a base and then fill in the hole to be even.

While lime putty plaster is to hard to sand effectively, there are setting drywall compounds (Easysand) that make excellent repairs and can be sanded.

Do not try to use plaster of Paris, or even the 'patching plaster' sold in stores.
Both harden way to quickly to be useful.

So you open the wall and find the leak in a 1958 bath. I would say that you are dealing with concrete on a wire mesh, not fun. 4" right angle grinder w/ a quality masonry disk should go through concrete and mesh.
Chances are there is a three halve system which is probably exhausted its design life and is no longer acceptable by today's standards. This ain't gonna be a cheap repair.