1. You take your time
2. Use the proper tools.
3. Plaster wall on the other side is in good condition.
I would attempt to find the studs with a stud finder. The I'd cut an opening in the center of where you want the cabinet to be placed. (big enough to look into with a flashlight.
I would use a "Saws-all" or a skillsaw if room allows. Skill-saw with a metal blade should cut this without to much of a problem. (Messy)
I would then check to see what's in the wall. You will need to install studs above and below the cabinet anyway.
If you have the proper room to to this then you can continue with the install.
If not you can re-install the piece you removed and re-plaster the edges.
Make sure there are no wires aroud the area your working. (Not good if you cut the power lines)
Just remember to set the depth of the saw to only cut the thicknes of the plaster and backing, not the depth of the blade, or you will cut through both side of the wall. (Important if using the "Saws-All")