Karst is my least-favorite material to drill through, because you never know what you may find. You can drill through hundreds of feet of essentially solid rock, then move over 20 feet and drill into a cavern. I was at one site where a drill rig set up about 100 feet from a major highway, began drilling, got down about 2 feet, and then the drill rods dropped the full length of the rods (20 feet). They scrambled off that location and ended up dumping a truck's worth of gravel in the hole to stabilize it and fill the boring.
Another problem is the necessity of drilling beyond a big void without letting that giant pool of (possibly) contaminated water flow downward to mess up (possibly) clean material below. In that scenario, we usually telescope casing. That is, start drilling with a larger diameter bit, say 10- or 12-inch. Drill down to the big void and set casing through it and seated into the rock below. Make sure you are well seated (at least a couple feet) so that you can pump cement down there. You'll likely need a special plug so that you can pump cement down the inside of the casing and force it out to the outside. Once everything is sealed, re-start drilling and repeat the process with the drill bit that's a size smaller. Repeat process for each big void and hope you don't need to telescope too often to get where you need to go. If you guess wrong and don't start with a large enough borehole in the first place, you'll need to drill another, wider hole and start the process all over again.
Water control is another big problem. The fastest and cheapest way to drill through relatively hard material like limestone is to use air-rotary drilling, where you blast compressed air down the borehole while a drill bit chews away at the rock. Air, rock chips, and water get sprayed back out the top of the borehole, where it is contained by a big contraption that allows everything to fall out and not cause a complete mess. The material collects in a mud tub, which is regularly shoveled (solids) and pumped (water) to drums or holding tanks. However, if you hit a big water-filled void of contaminated water, you can get 200 gpm or more that you need to be able to contain and pump, and somewhere to pump it to. So air-rotary drilling may not be the best application. An alternative is cable-tool drilling, where a heavy bit free-falls and then the little broken-up rock pieces are bailed out of the borehole. Cable-tool drilling is painfully slow, and hardly anyone does it anymore in the areas I work in, so the pool of (antique) drill rigs available and drillers familiar with them is small.
I always err on the side of caution when I'm in an area known to have big voids. But if everything goes well and we don't hit much of anything, then I get an earful about why we spent so much time and money on giant boreholes or slow drilling methods. And why, exactly, we have a bunch of 20,000-gallon tanks for a couple of piddling boreholes. This is the part where having a manager or client with a basic understanding of geology really helps.