I had earned the platinum trophy for Borderlands 2 on my PS4, and I have the same game for the PlayStation Vita.
How can I transfer my data so the platinum trophy will pop on the Vita, as well?
This is game dependent, some games share a trophy list across PS4 and PS Vita, so unlocking a trophy one one device will also unlock it on another. This is particularly true for games that are "cross-buy".
Other games have separate trophy lists, which means unlocking on one platform won't affect the other. Minecraft is an example of this, where each version has a independent list. And even though you can transfer the save data between the games, it won't retrospectively unlock the trophies you've previously unlocked.