Guard Cancelling.
Guard cancelling basically put is just tapping the Guard button, to reduce the Lag, and this can speed up how quickly Dante goes on offense. Well why tap? Basically because it puts Dante back in his normal stance more quickly, although you have to be a Fast clicker or you have to time it right. In order to Get Dante to sucessfully block the attack and go straight back to offense.
Switch Cancelling.
Nearly all the Guns have a time Lag between each shot. To my knowledge the only one that doesn't is Ebony and Ivory. Yes even the shotgun has a time Lag, even when they are up to max Level. So, this is how to avoid the time lag, you can cancel it one of two ways. The first would be by Jumping straight after you have fired the weapon, although this will not work as well, it is still effective. The bad thing about this is that if you are using a weapon such as Spiral or Kilina Ann, then they can't fire while being airbourne. But others such as the Shotgun or Artemis can, so you would be fine on those. I personally don't use this technique that much, I prefer to use the second choice as it offers more control, and you can fire faster, and after all that is what it is all about.
Now the second choice is to press L2 twice, in order to switch your Guns back to the one you were using. Now yes this takes the time lag off, but you have to be fast pressing to make up for the time lag. Otherwise you may as well wait for the Gun to reload. This is the one I prefer using as it offers more control, and you remain on the floor with it. And if you can press it fast enough you can build up a good style meter. Now there is another way to cancel the time lag, but this one is not as useful. The other way to do so, is to perform a Devil arm melee attack, this cancels it, but then you have the time lag of that attack. If you are going to use this way, I recommend using Cerberus as it is fast paced.
I always recommend having Ebony and Ivory in your Gun inventory, because if you are using the Switch Cancel by pressing L2 to get rid of the Lag, you can keep on firing this Gun for the Ultimate Projectile onslaught. This could result in a load of Stylish points added at the end of the level, just by knowing this simple cancellation of Guns. Great isn't it?
And probably the one you have been hearing about..
Jump Cancelling.
Basically if you perform an aerial attack, with either Vergil or Dante, and you are nearby an enemy, you can jump off them by pressing X, and this also restarts your Jump, which means you can do the attack again. Using this, you can get some serious style points, and keep enemies in the air for a decent amount of time.
Basic examples of this, is Vergil's Aerial Rave, if you hit an enemy up into the air, using an upward slash, and then jump and start to attack, you can use this technique to do multiple attacks in the air. Another Example, is Cerberus' Revolver attack, this is fast paced just like aerial rave, so you have to be quick to press X then triangle, and repeat.
Easier examples of this are Starfall, or Killler Bee, when you it then you immediately press X and then you rebound back up in the air to do another Killer Bee, or Starfall (depending on which character you are using). Using the Jump cancelling technique can be useful, but has to be learnt in order to do it to its full potential.
If you need extra advice on this one, you can go to Broly2012's Jump Cancelling tutorial.
Hope I helped. :)))