How do you delete individual texts from a message conversation in iOS 8?

Solution 1:

Press and hold the message to delete, a menu will pop-up with the options "Copy" and "More". Tap "More".

Press and hold the message to delete, select more

The message you selected is marked with a checkmark on the left. You can check more or delete all by tapping "Delete All" on the top left.

You can select more individual messages if you will, or delete them all

Tap the trash after selecting the message to be deleted. A confirmation will appear. Press "Delete Message".

After tapping the trash can

The message is gone. Just blurry messages are left.

Individual message deleted