Probably over 20 years ago I broke a tap off in a project I had significant time and dollars into. I added to the cost by destroying an utterly useless Walton tap extractor (has anyone *ever* had one of those work? - I think they're worthless) followed by a couple of carbide drills (which are normally successful). After that I took up a study of tapping. I learned a lot, but the takeaways that really mattered are: use a high quality tap (not Irwin or Vermont American, or whatever is being sold at your local big box store) and get it started straight. Quality wrenches or tap holders are probably third on the list. I then went about 20 years without breaking a tap, until I tried tapping #2-56 x 3/8" in 17-4 PH. I forgive myself for breaking those (yes, multiples...).
GsT