First, an idol in the unit needs to have the Burst Counter skill (under バーストカウンター should be a ○), if you don't you can't do it at all. If you have it, after a rival burst activates, quickly fill yours up (a general tip is to fill up first and then wait patiently for the AI to get fed up with waiting to counter you and then use a memory) and activate your burst before theirs ends. you'll see "burst counter" come up on the screen if you did it right.
Also, all the trophies are translated up on the english wiki owo they're all in order they're listed in the trophy listing.
I'll also note a couple of other points.
1. Counter bursting has a multiplier associated with it. You score more points on your burst if you successfully land the burst in question.
2. An opponents burst is not considered completed until:
a) The opponent's burst bar is empty and
b) You fail to conduct a burst, be in a hold state, or a burst evolving action. This means in fact you can in fact counter with a triple burst, but you have to have a full bar, then appeal twice more more or less immediately after you hit burst status.
The second condition is a little more complicated.
Basically, as long as you appeal, or burst the first opportunity you have, just before the end of the rival bar emptying (Basically, the words 'Burst ended/complete' show up) you're allowed to mount a counter burst.
