I've noticed that when fighting a group of enemies, only on the last enemy you kill can an
animation be triggered. The only exception to that is during the "imperial/stormcloak"
questline, when you are battling the other side, it seems that animation kills can be
triggered eventhough several enemies are still left.

Also i've noticed that being on even ground as your enemy helps a lot in triggering the
animation kill. If either one of you are on a slope, or even on a rock it seems to
interfere with the trigger and all you'll get is a boring standard kill. So try to lure
your enemy in an area where the ground is even, in the case of archers and mages, get
close enough to them that they'll draw their melee weapons then you can lure them to a
preferable area.

It also helps to be in front of your enemy, if you attack him/her from the side you won't
trigger the animation, try to position yourself right in front or behind them for greater
success.

Also, if your enemy is blocking it will never or very rarely trigger the animation kill.

Same if an enemy is using, say, an enchanting alter or a tanning rack etc. If you kill
them while they are "busy" with an object you will never trigger the animation.

I've also noticed that pressing towards your enemy with the analog stick can help trigger
the animation kill. Try to attack them while they are either not blocking or while they
are launching their attack.

Different weapons trigger less often, i've had trouble with maces, they also have fewer
animations.

Same with enemies, skeletons and skeevers come to mind, these enemies either have no
animation or they trigger very rarely.

Stealth kills always trigger, you can use that to your advantage. Sneak behind your enemy
and when you are ready for the kill quickly stand up and attack them, if no other enemy is
around you'll trigger the animation kill. If an enemy is alone and has heard you but not
detected you yet, you can wait for them to walk up to you and attack them when they are in
range, that also has a high chance of triggering the animation kill. Needless to say, if
you remain hidden and in sneak mode you'll have a "stealth" kill animation.

The stronger your weapon the more easy it'll be to trigger these animation kills, i've
noticed with my games. If the kill is an outright "overkill" triggering the animation kill
is very common.

You can trigger an animation even if the person is busy but its is quiet rare ive only
doen ita a few tiems myself.and for dragons you must hit them on teh side of the head or
front adn you'll jump ontop and do that animation thing.and skeletons can get an animation
kill but its rare with a melee weapon,skeevers might have one but it'd be extremly low.