Here you go.
1, Open messages to the conversation screen.
2, On one of the messages you want to delete, flick up and double tap more. This will select that message and put you in select mode.
3, Just swipe through your messages in the conversation and double tap the messages you want to delete. It will select each of the messages you double tap.
4, Once all the messages are selected that you want to delete, go to the bottom of the screen and you will find a delete button.
5, After they have been deleted, you might have to hit the cancel button at the top to exit select mode.
Hope this helps.
Chris