1. extreme (measure, idea, etc.); radical; violent (language)
けれど彼はちょっと過激だな。But he's a bit radical.
2. strenuous (exercise, work, etc.); excessive; (physically) demanding
最近は修行も過激さを増し、昼間でも眠くなることが多い。Lately my training has gotten more intense, and I often get sleepy even during the day.