What I find helps is to watch the ATB gauge and listen for when the attack hits and that is when I cue the next attack. It will take time and a lot of practice but you will eventually get it.

The HD version has no stun locking since we do not use the girls.

When 1 attack animation finishes start another one its just a rhythm

also the stunlock is most difficult to do on the Kilika boss at the end of Ch1 as it has very little leeway to allow for mistakes in timing. so if its' only happening on that boss then it's to be expected and your chaining will get better with time.