Avoid 1 Hit KO Strategy (Normal)
Every few seconds, one of the arms is chosen at random to attack. This means that, as you kill arms, any that are left alive will attack more often. The final arm will attack almost constantly. This means that an effective strategy is to prioritize arms in descending order of damage. As long as you have sufficient food to survive getting hit by the weaker arms, leaving them free to attack can reduce the odds that you get hit by the more powerful arms.
For all classes, Bottom Left should be the first that you destroy. The fact that it is both a one hit KO and ranged makes it extremely dangerous when it attacks quickly.
As a melee class, Top Right should be your next target. You want to continue to minimize the potential for a one hit KO. If you are a ranged class, you can save this arm for last since it can't hit you.
Next, kill Top Left. Depending on your armor, this arm could kill you in one shot as well. Be cautious if you aren't sporting Amarok armor or have low health.
The remaining three arms do little enough damage that they can be tanked with food. To minimize damage, go for Middle Right, then Middle Left, and finally kill Bottom Right.
The following was done with a Birch Longbow with 170 range. Any better bow with more range may make things easier.
It's recommended you start with Middle Left Arm first since the Blue Flame Orb will constantly be casting and you will need to dodge while killing the other arms. Be careful though because the Hammer can hit you while you are attacking - watch for the hammer spin to avoid. You can then kill the Middle Right Arm by just firing away so you can take your time on the other 4 arms.
Both the Top Left Arm and Bottom Left Arm can hit you as an Archer with Birch Longbow so watch the timing and kill carefully. You want to run in, fire a few arrows, watch for the triggers, run away, and repeat. If you struggle with the timing, you can stand at the back of the Platform and spam ranged skills like Homing Arrows and Piercing Arrow.
Both the Top Right Arm and Bottom Right Arm cannot hit you if you stand the proper distance. Fire away and kill.
Once the 6 arms are dead, the Armor buff is gone from Efaunt's Head. Finish him off, dodging the blue rings and healing as necessary. If it helps, you can stand back and spam skills to better avoid the blue rings.
Using the lower 150 range Wooden Bow, all the same strategy applies. Though the Scimitar attack can now attack you when you are in normal attack range for the Top Right Arm.
The following was done with a Steel Axe with 62 range. Any better melee weapon with more range may make things easier.
Study the attack patterns described above because all attacks can hit you when within a melee range. You will be running in, getting a few attacks in, watch for the imminent attack, run away, and repeat.
Prefer you start with the Middle Left Arm so you can do the other arms at a bit more leisure. Careful as the Hammer swing will hit and kill you, even with 1,500 health.
Move on to the Middle Right Arm so you no longer need to avoid the purple rings. Careful as the Scimitar will hit you if you are attacking the arm.
The Top Left Arm, Bottom Left Arm, and Top Right Arm are all One Hit KO's at the range you need to stand to attack so watch the arms carefully. You could switch to a Wooden Bow but that would only protect you against the Top Right. It's all about timing.
I'm leaving the Bottom Right Arm last as its the least damaging and in my mind the easiest. Finish it off.
Finally the Head is available to attack. Wail away at the head, dodging blue rings and taking a break to heal if necessary.
Low-Risk Barbarian Strategy
The Bear Swipe and Axe Hurl talents can hit opponents above you. This works best with a high level in either skill.
Destroy Middle Left then Middle Right as normal.
Now Top Left is the only arm which can hurt you. Carefully destroy it in the normal way. Do not leave it until last or it'll attack frequently.
From here, the fight is won. Stand under Bottom Left and Top right and fight them with either Bear Swipe or Axe Hurl (or both). Bottom Right is not damaging, neither is the Head.
Low-Risk Squire Strategy
Get decent levels in Daggerang and Shockwave Slash for this.
Confront the Middle Right arm first and destroy as quickly as possible. Use Shockwave Slash to hit Middle Right, but don't destroy Bottom Right just yet.
Run to the small platform on the left side, as nothing can hit you there. Shockwave Slash takes out the Bottom Left and Bottom Right. Daggerang hits Middle Left. At this point the upper arms should be at full health and the Middle Left at about half.
Run up the rope and behind the lantern. Make sure the hammer is not twirling or swinging and you should have time. Daggerang hits Middle Left and Shockwave Slash hits Upper Right and Upper Left. Now the head is attackable.
If you only have a Gnarled Wand or Quarterstaff equipped on your mage, it is dangerous as those have 115/120 range. Recommend you equip the Wooden Bow instead with 150 range. This will allow you to follow a similar strategy as the Archer Strategy, albeit spamming different skills.
Using the Wooden Bow or higher tier Mage weapons like Starlight or Crow's Nest, you can emulate a similar strategy as the Archer strategy. Fireball lets you attack from the back of the platform, similar to Piercing Arrow.
Low-Risk Shaman Strategy
If you have a Shaman with a leveled Crazy Concoctions talent, you can cheese your way through this boss. The Bottom Left Arm can be attacked by standing on the platform below and throwing the potion above. You can also stand at the back of most of the Platforms and attack all arms.