I'll have to agree with Andrew on the FW dips...won't do much good other than stressing the fish out even MORE at this point. In the past, the only time we have experienced severe Ich breakouts in our tank(s) is when the stress levels were too high (especially territory issues). I don't know what size tank you have all these tangs in (six tangs, right?) but depending on what order you put them in the tank, and how long it has been since everybody "staked out their territory", with the information you've given, I would say the addition of the Achillies is what is causing your problem. Not b/c the Achillies had ich, but because there is no longer sufficient room for all your fish to feel comfy/have their own territory. You may feel you have enough water volume, but where are they all sleeping at night? What spot do they run to in the daytime when they are spooked? Do all fish have PLENTY of hiding space without encroaching on another tang's "space"? Have you noticed any of them display increased aggression (tail slapping/chasing)? Not to mention that Achillies are ich magnets anyway >_<

Cleaner shrimp will "help", but they won't be able to keep up with the outbreak of all your fish.

I had this very same thing happen before my hubby and I upgraded to our current 210G display...added an Atlantic Blue tang to a tank (75G) that was a tad crowded, but I knew we would be upgrading soon so I thought everybody could co-exist for a month before the upgrade took place. To make a long story short, we lost SIX fish due to that incident.
To be quite honest, I'd say you have two options at this point...upgrade to a bigger tank with more room for your fish, or get rid of the Achillies. Sorry to be the bearer of bad news. :(
Hope everything turns out OK. ;)

W.