be careful, hard, strive
劼 centers on careful, determined effort: being meticulous, working hard, and striving persistently.
劼 combines 吉 (good fortune, auspicious) and 力 (strength, effort), suggesting careful or strenuous effort toward a good outcome. The exact historical development is uncertain.
The left side 吉 looks like a lucky charm, and the right side 力 is strength. Imagine carefully polishing a lucky charm with all your strength, striving to make it shine.
For カツ, picture a cat carefully pawing at a lucky charm, striving to knock it over: cat -> カツ, and the cat's careful effort matches the kanji's meaning.