I am trying to understand how the Body Guard talent (and others like it) function.

It says to upgrade difficulty of attackers, but doesn't say if that will be an extra D8 difficulty die, or should I upgrade an existing difficulty die to a D12 challenge die?

When you upgrade the difficulty you would change a purple Difficulty dice (D8), into a red Challenge dice (D12). If there are not purple Difficulty dice (D8) to upgrade, THEN you would add a new purple Difficulty dice (D8) to the roll.

I just wanted to make sure since the text next to the red die in the Force and Destiny book mentions the DM can add the die, so I was concerned that it's the only way it happens.

FaD pp. 29-30 go into detail about upgrading and downgrading dice pools.

The language of the official books is:

"Upgrade" always means taking a green/purple and changing it to a yellow/red. If there are no green/purples to upgrade, then you add one instead.

"Increase" always means add an additional dice to the pool.