Piercing caverns isn't tough, once you realize that stairs are an amazing upside-down construction. You can breach a cavern from the roof, and then build a stairway down into open air, with your worker standing on the level above as he builds the next stair down. Stairs can support floors and walls as well, so you can build the stairs, and then walls around it, without even touching the floor. It's just important to note the direction of building facing, and diagonals. In general, you'll want to build your walls like this...
First:
.F.F.
.FFF.
.FXF.
.FFF.
.F.F.
Where F = floor, X = Stairs, . = Open Space, and W = Wall.
Second:
WF.FW
WFFFW
WFXFW
WFFFW
WF.FW
You must do this, so that you can build the corner walls, otherwise it'll be out of reach of your buildings and any flying creature (and they DO fly!) can sweep in undisturbed.
Third, skipping the diagrams now, you simply un-build those for extra floor bits, and replace them with wall bits, so that you end up with a floor surrounded by walls. Then, repeat for the next level.
Just be careful how you build the walls. Constructions are produced in "First in - last out" order, so the first one you assign to be built will be the last one finished, as long as you don't unpause while designating construction. And because dwarves build things from predictable directions, you should always build the South or East wall LAST, since they build from the west or north on these. If you build the west wall last, they'll stand on the outside of your perimeter and wall themselves off.