It was literally Kim Potter's defense. Shooting was an accident and untentional, but she was within her rights to use deadly force.
If some charge requires both [A] and [B] for the accused to be guilty, then this argument is that it's neither [A] nor [B], but the defendant is innocent if they can prove either half of the argument, since the condition is "[A] and [B]", not "[A] or [B]".
No, you don't.
It's just if you are charged with an offense that requires intent, the question of self-defense (or any other excuse) is moot if the prosecutor can't prove intent beyond a reasonable doubt in the first place.
If you are charged with an offense that doesn't require intent, like involuntary manslaughter, you don't have to argue intent to kill to use self-defense as an excuse.
And even of you are charged with an intent crime, you don't need to grant intent to argue self-defense.