He has intangability. Before the acid can injure him all, he become intangible to throw the acid out of his body.
Before the cat can make his next move, Barbas reads the cat's greatest fear. After he findsd cat's greatest fear, he manifested it into the real world, making it come to true. As the cat sees the greatest fear cone to life, where he keeps telling himself "this is NOT happening" stress out, (s)he becomes paralyse of it, making him vulnerable to do any other attack to Barbas (or free himself for that matter), unless pray for help and just hope for it to go away...
Barbas just waits, for the cat to get a heart attack of the amout of fright he is getting.
Unfortunately, Dex-Star has already seen it's worst fear. And unfortunately for you, you just started resembling it.
I would recommend you to read Dex-Star's origin story, simply so you know how pissed off you just made a Red Lantern.
And this Cat doesn't get angry normally. It's anger is without emotion, it's anger is calm, it stays completely collected. It is practically evil, regardless of the cause of the Anger.
And you just started Resembling the thug that broke into Dex-Starr's house and killed his owner. Of course, you are screwed.
Also, he is unable to utter spells as the hair all practically destroyed his mouth.
Yeah, you are pretty screwed.
And yeah, Anger and Fear usually aren't conflicting emotions. Fear usually gives rise to Anger.
Dex-Starr Annilates Barbas by making the ground beneath Barbas's very feet intangible.
Barbas is forced to stay in intangible mode until he either dies from hunger, thirst or falls into some lava or the molten center of the earth.
Of course, he might eventually find a cave, but if he finds one too fast he might cripple himself from falling, if he finds one too slow he is probably dieing from starvation or thirst.