I think it´s like this, at least it always works when I´m doing it:

1/1 - initial Limit Break
1/2 - use 1/1 eight times

2/1 - kill 80 enemies
2/2 - use 2/1 six times

3/1 - kill 80 enemies
3/2 - use 3/1 six times

Something like that.
However, numbers of needed enemy defeats seem to vary a lot,
I´ve heard of some chars having to finish 96 enemies and stuff like that.
But this is pretty much how it goes.