Specing in speech (obviously) grants more options.
Just like the other skills, when they all reach 50, you can spec your favourite.
During conversations you'll come across skill challenges, just like those in other RPGs like Fallout.
common ones are:
•Persuade
•Lie
•Imtimidate
Other than those, there are ones linked to other skill types such as:
•Medicene
•Engineering
•Melee
Anything that comes up with an option in square brackets, e.g. [25 Engineering] or [60 Persuade] counts to this trophy. Successfully pass thirty of these and it'll unlock.