The achievement is unlocked when you deliver five consecutive hits
with a weapon (not an ability) against an airborne target. Although the description states, "a launched enemy," strikes against any airborne enemy count towards the achievement.
Certain weapons can launch enemies like the Longsword's upheaval attack (

pause

--assuming the Longsword is the primary weapon) or the Greatsword's Gut Thrust (Perfect parry with

immediately followed by

assuming the Greatsword is in the primary weapon slot). After launching the enemy with the primary weapon switch to a fast strike secondary weapon.
The longbow auto-aims so pressing

five times in quick succession will deliver five consecutive strikes against the enemy. The Chakrams are dual weapons with spinning blades that deliver multiple hits in quick succession. Pressing

once with the Chakrams in the secondary weapon slot should deliver more than five consecutive hits providing the enemy is within range. Chakrams are a mid-range weapon and don't have the same reach as the longbow. Daggers are a little trickier. You must press

in the direction of the enemy and rapidly press

. Each dagger in the pair counts so three strikes will deliver six consecutive hits. Daggers are a melee weapon so you must lunge close to the launched enemy.
These techniques require moderate hand and eye coordination. When you have 50 skill points in sorcery, you can unlock Orbit Blades for the Chakrams. With Chakrams in the primary weapon position press

immediately followed by

. The Chakrams will both launch the enemy and automatically deliver a barrage of spinning hits unlocking the achievement.
Perhaps the simplest way is to strike against an airborne enemy like a mage. Three strikes with daggers (you need have no dagger mastery) will deliver six consecutive hits and unlock the achievement as shown in the video below: