Attacking an enemy while descending from a jump counts as a critical strike, which will do double damage. When you properly execute a critical strike, several small dark-yellow pixels will splash out from the monster.
It's worth noting that ONE heart is worth TWO damage points, so doing 9 hearts of damage means dealing 18 total points of damage. Also note that the monster you are fighting must have at least 18 hit points in order to receive the trophy. Horses generally have more HP than 18, as do some mobs while in hard-mode difficulty.
Critical strikes with a diamond sword enchanted with "Sharpness II" should do the trick.