Volazj's quick demise is easiest with a protection warrior tanking the boss. Volazj's mind flay can be Spell Reflected for considerable damage.
It is possible to complete the achievement just by nuking the boss and killing the illusions made from the two insanities as quickly as possible. Other tactics include heavy nuke on the boss when he casts the first insanity, bringing him from 66% to 33% before he finishes the cast, he will then start to cast the second insanity and needs to be killed before he finishes the cast or the party will be faced with 10 copies per person (instead of 5). Another viable tactic is to have the healer suicide (preferably just after the first insanity). This will make the second insanity much easier due to having 9 copies less to deal with, however this tactic does require a good geared warrior tank and probably the use of health pots.
Now that dual specs is out, having the healer switch to DPS makes this achievement quick and painless. If no one in the group is specced for healing the shadows will go down quickly. Be careful not to get Volazj below 33% before he finishes the first Insanity cast. As soon as that first set of shadows is dead, blow all your cooldowns and with 4 DPSers he should be dead before he can finish casting the second Insanity.