To perform a critical edge you must use up a full bar of meter from your Critical Gauge. To build the meter you must give or receive damage in battle, if your opponent is on the last round before winning the match your Critical Gauge will refill by one full meter. Critical Gauge inputs are the same for every character, it is down with the following input:++.
Against most low level A.I's, CPU raw Critical Edge attacks will hit them however most of the time you want to hit confirm into it, on the off chance it does get blocked it would mean you wasted a bar of meter. Under each characters basic combos listed in there move list is a a hit confirm combo into there Critical Edge most of each consist of inputs.
If you do not feel up to grinding this out in any of the offline modes, you can boost this with a partner online. If you are having trouble finding a partner please refer to the Trophy Boosting Thread.