I would recommend having a boolean called something like animation_locked. Then when you play an attack animation, you set the boolean to true. If the boolean is true, then you let the animation play by adding conditions that check if animation_locked == false before changing the animation. That should prevent another animation from overriding the currently playing animation.
To unlock the animation, I would suggest connecting the animation_finished signal from the AnimationPlayer node and in the function the signal is connected to, set animation_locked to false when the animation is finished.
Its perhaps not the best solution, but I have used this method several times without too much difficulty.
You could also look into using a state machine for your player and let each state in the machine handle its animations. Then with a state machine, you would just stay in the attack state until the animation is finished. It is a bit more complicated to setup though.
