You can view the required actions for ACE points when you pause the game. They are:

Assault ACE Points
+3 Kill an enemy or player behind cover with penetrating weapons.
+3 Kill an enemy or player with C4 (it must be C4)
+2 Kill an enemy or player who is using a mounted machinegun
+2 Kill an enemy or player with a frag grenade or breaching charge (i.e., something that's not C4)
+2 Kill an enemy or player who is using a riot shield

Marksmanship ACE Points
+3 Kill an enemy or player at long range (about the size of your targeting circle at its widest diameter)
+3 Kill an enemy or player when they are on a rope (fast rope or rappelling)
+2 Kill an enemy or player while you are rappelling
+2 Kill an enemy or player who is sprinting
+1 Kill an enemy or player with a headshot (any weapon, although a long distance headshot will result in a long distance kill instead)

Close Combat ACE Points
+3 Kill an enemy or player at short range (their height should be a third to half of the size of your screen on either standard or hi-def)
+3 Kill an enemy or player who is stunned or flashbanged (vision impaired)
+3 Kill an enemy or player by blind-fire (this range may be slightly more than the short range kill distance)
+3 Kill an enemy or player from behind (distance may change this to a long range kill)