Literally: firmly – harden – one – pierce
Alternately: Obstinate. Stubbornly sticking to one’s views or ideas. Pushing one’s vision through in spite of all opposition or resistance. Alternately, a person with that sort of stubbornness.
Notes: Both 頑固 and 一徹 mean “stubborn” on their own, so this is a yojijukugo that emphasizes its content through repetition.
Apparently some people accidentally replace 徹 with homophone 撤 (“removal”) in handwriting; this is an error.