All optional conversations in chapter 4 occur after unlocking the four ruin locations at the central tower.
The first is prompted by your arrival at Shiva’s ruin in the north, marked by the axe. Approach the doors to have Chloe and Nadine start talking, to which Nadine will eventually have a speech bubble appear over her head.
Activate the optional conversation by pressing triangle. The conversations don’t stay for long, so make sure to keep your eye on them if you’re looking to pick them all up.
The second conversation will occur at the ruin in the far southeast, marked by Ganesh’s trident.
Same as before, approach the doors to the ruin to have Chloe and Nadine converse. Then press triangle again when the speech bubble appears over Nadine.
Head to the ruin of Parashurama in the southwest, marked by a bow and arrow. Once again, approach the doors and wait for the speech bubble to appear.
The last optional conversation happens once you have collected all 11 Hoysala tokens and made your way through the token ruin to the monkeys.
Head on over to the pillar in the back right, behind the ruin, and press triangle to inspect the monkeys and have Nadine come over and prompt you with the speech bubble again.