There are two rules that all party characters follow when it comes to triggering a character's story segments.

1) the number of times they have been deployed.

This requirement is based on the combination of story battles, mock battles and replaying of previously completed story battles. As I tested the mechanics on characters with 2 story segments (beginning & end), the requirements for those with three segments might be higher.

To trigger the first story segment you'll need to have at least 10 deployments; for the second segment a minimum of 20 deployments. Based off of this, I'd expect a third cut-scene to require a minimum of 30 deployments. However, none of the late game (chapter 15+) route specific characters have 3 cut-scenes.

Note The character only has to be deployed; there is no requirement for them to achieve kills, provide healing or for them to survive the deployment.

2) the story must have reached a specific chapter.

This is a variable factor, which depends on the character in question as to when the cut-scene will trigger, as their side story is tied to main story events. If the key event hasn't happened yet, then their cut scene won't play.

It is important to note, the earliest you can trigger the cut-scenes is one chapter after the character joins your party. I managed this with several of the chapter 15 route specific characters, whereby I unlocked the cut-scenes & achievement before playing the chapter 16 story mission by simply grinding level 3 mock battles.

Regarding Avorla , you will need to be on the golden route in order to trigger her cut scenes. I did try to unlock the second scene whilst going for a standard ending, but couldn't trigger them as she hadn't formally joined the party.

To view her 2 scenes you need to have deployed her 20 times, between the regimental battle in chapter 18 prior to the start of the final battle in chapter 21. The cut scenes can be viewed as early as chapter 19, prior to the story battle.

If you have already completed the golden route, and don't wish to replay that story arc in full again then there is a work around. You will need a save file from the golden route, at any point between chapter 18 and the final battle. You simply grind the deployment counter to 20 with mock battles of your choice and watch the two cut scenes. This will then trigger the achievement. You are not required to have viewed all the stories on the one save file for your achievements.

This should hopefully help people who are trying to get all story achievements for Travis, Trish, Cordelia, Milo & Avorla.