How to delete messages taking up space on iPhone?

Is there a way to do it without a factory reset or erasing all data?

Added (1). Saved message taken up 200mb.

In the messages screen where you can view your conversations, swipe left on a conversation and press delete.

There are two ways, the first is exactly like Cole said. Swipe your finger to the left on the messages with a particular person you want to delete, and then click the red delete button.

The other way is to click "edit" in the top left corner of the conversations screen. Then click the red circle and then delete.