The “Swipe QTE” — to complete it you just need to swipe in the direction of the arrows before they run away.

You need to tap the icon of a character in order to use his/her ability in the battle. 

For the QTE with the green burning circle, you need just to tap at the right time before the circle disappears completely.

For the QTE with a white line and a green middle, you need just to tap the screen when the white mark hits the green zone.

For the QTE with a red circle, you need to tap right when the yellow circle hits the red circle. If you hit the red circle then you get critical damage. If you hit yellow circle then you get the same damage as from usual QTE.