What level are you doing this mission at? It has been uncapped for quite some time, so there should be no reason it is unsoloable unless you are purposely going in at level 25 (which I believe was the old cap).
I'm not trying to discourage you from playing with groups - but this isn't the nightmare it used to be.
____________________________On the topic of Black Mage in XIV:
They summon fireballs and fart lightning. From their eyes.
Even thinking about them makes enemies explode.
Having one in your PT is like a free ticket to defeat Absolute Virtue.
That's the reason why only one of them is allowed in PvP. Per server.
Imagine a cross-breed between Allakhazam and Sun Zu. That's a Black Mages's toenail.