When I first cultured AX, I was given Bactrim (now resistant), and then later during a hospital stay I was given ertapenem and imipenem.
During my hospital stay I did get much better, however the following year my AX was resistant to all of the 'penem series.
I've been on Augmentin (a combination of Amoxicillin (b-lactam antibiotic) with potassium clavulanate (b-lactamase inhibitor)), which has seemed to work well.
b-lactam antibiotics and b-lactamase inhibitors are almost always used in treating Alcaligenes (achromobacter).
I've cultured multiple strands of AX (some at the same time) ever since 2001. It has never been eradicated and my doctor told me that most likely I'll have remnants of it for the rest of my life.
I don't want to sound discouraging or anything.. but its a pretty stubborn bug. lol