I've encountered this problem many times with Delta faucets. I have developed a simple and reliable technique for repairing even the most stubborn ones.
Before beginning, make sure you have a replacement cap. The Danco 88756 cap
fits Delta kitchen and lavatory faucets I have encountered.
Using a Dremel tool with a cut-off wheel, cut a vertical groove into the cap. Be sure to wear eye protection, and I recommend positioning a vacuum cleaner hose near the cut to collect debris. Cut as deeply as possible without cutting into the faucet body. If you do cut into the body, it's usually not a big deal as long as you don't go all the way through. I usually nick the body a little.
Put a flat blade screwdriver in the groove and twist/pry until the cap breaks along the grove. If it won't break, cut the groove a little deeper and repeat until it breaks. The cap will now unscrew.