I would just put a hit box around whatever weapon your character is using, whether it’s a sword or his fists. Then just use a touch sensor to see when it touches an enemy.
You could also do some creative things to determine the amount of damage a hit should do. For example, if you want a sword swing to do very little damage during the begining and end of the animation but have a high damage “sweet spot” in the middle, you could use a timer property. Just start the timer at 0 when the player starts the animation, and when the weapon hits, use the equation <damage delt> = <peak damage> - <peak damage>/(<animation length>/2)^2 * (<timer> - <animation length>/2)^2
Just make sure you don’t deal any damage before the animation starts or after it finishes.