(updated 5-5-13 with extensive revisions to with the exact cost progression of heads, and concomitant update to economical acquisition strategies)
This achievement is for acquiring all of the prisoner heads. This achievement does not count special heads (the star category), it only counts the four regular types: circle, triangle, square, rectangle. There are 64 heads of each type and thus 256 total heads. The heads can be acquired by purchase from the vending machines in the gift shop area, or via trade form another player. For each type of head there is one default “blank” head that is untradeable (you always have it), the other 63 can be traded. In order to pop the achievement you must possess all heads at one time, acquiring a head and then trading it away will not make progress towards the achievement.
The gift shop sell the heads from four vending machines sorted by type. These machines cost gems, starting at 10 gems and increasing based on how many heads of that type and total that you currently have (more on prices in the next paragraph). When you purchase a head it gives you a random unacquired head of that shape.
Head cost seems initially confusing but upon further testing proved to be fairly straightforward. The cost of new heads depends upon how many total heads (counting blank ones) you own, based on the following table:
4-59 heads: 10 gems
60-119 heads: 15 gems
120-179 heads: 20 gems
180-239 heads: 25 gems
240-255 heads: 30 gems
Note that 'star heads' do not count into this calculation at all. Additionally if you have too many of one head type then the price for that head type may be higher than the price for other heads. This system seems to be in place to raise the price if you try and buy different heads types on different profiles.
1-29 one type: 10 gems minimum
30-59 one type: 15 gems minimum
60-63 one type: 20 gems minimum
To buy all of the heads and get this achievement will take a large number of gems based upon the method used. You can buy each head type in turn, though this will be the most expensive way as you are paying the premium on the first head type. Total cost of this sequential method is 4795. Alternately, you can buy heads from enough different types so that you avoid the premium pricing (ie never buy heads at 15 or 20 if other heads types are offered for less). Total cost of this ‘smart’ strategy is 4640 and this is the minimum without using multiple accounts or getting heads in trade. Finally the last and cheapest way is to create three additional profiles and buy each head type separately (the main will buy the first head type) and then trade the heads to your main at the end. This will cost 820 gems per type you buy for a total of 3280. Note that you can discount the above prices by 40 if you intend to keep the starter non-blank heads you get.
How to get all these gems? Other than just through normal progression (which would be hard to estimate time), I identify three major ways to get gems, and calculate rate of earning gems:
regular arena mode: ~0.5-2.5 gems/min
local 4 player arena: ~10 gems/min
gem trade glitch: ~100 gems/min
If you just play single player arena matches, these typically last 2 minutes and you earn 1-5 gems, for a rate of 0.5-2.5 gems/min. If you have four local controllers, you can play the challenge mode (more than one player required to complete) in coop with all four players (detailed below) and earn 16 gems for every round of slightly <2min, for a rate of ~10 gems/min. Finally is the trade glitch which can earn 100 gems/min if you can execute 5 trades/min
The trade glitch can be exploited to get essentially infinite money fairly quickly. This may eventually get patched, but currently it works (I will try and update the solution if it ceases to work). What you need to do is to create an additional profile that will be basically an empty profile. Then trade away all the four starter heads that come on this profile until there are no heads. You cannot trade a head to a recipient who already has that head, so if your 'empty' profile happens to start with a head that your main acct has you may need to create a third profile to trade that head to so that your second profile can be empty. The next time you enter the trade window with this empty profile, it will automatically offer up 25 gems as trade. With your profile that is collecting the money trade 5 gems. This will result in setting the empty profile to 5 gems, while your money profile will have a net increase of 20 gems. Re-enter the trade window and the empty profile will offer up a 25 gem trade again and just execute the same 5 for 25 trade. This can be repeated as many times as you desire for a net gain of 20 gems per transaction (the reason you need to trade 5 gems is that without at least 5 gems the empty profile cannot enter the trade booth).
A couple other minor factors can speed things up. When executing trades, the cursor starts at the position of your current head. Therefore when doing the money generating trade it is advisable to have your head be the head that is directly below the 5 gems slot in order to more quickly (a cat circle head guy). If you are trading 0 gems (in order to transfer heads) you want the circle head that is directly below the 0 gems slot.
If you don’t want to do the trade glitch (or can’t because it has been patched out), the next best way is to use the 4 player arena coop challenges (multiple players required to complete level option). Sign in all four players to profiles (guests can’t trade), and play one of the easier levels. Generally you can get through 95% of the level completely solo, but there will be one spot where you need a second player to stand on something to make a platform appear, or throw you up to get a gem, etc. Play through the level as normal with one controller leaving the other three at the entrance. When you get to the two player section, suicide with a second player (to warp them to the closest checkpoint to you) and then use two controllers to get past the 2-player spot (this may require a bit of contortion), then finish the level as normal. You will earn 4 gems for each signed-in player, or 16 total.
With all this information, it is simple to calculate an estimated time to both earn enough gems to purchase all of the heads, and transfer all heads to your main profile in order to estimate how long it will take to get the achievement, and thus the best way to go about it. I assume 5 trades/min rate, and the gems/min rate in the above table:
buy mode gems cost trades time (glitch) time (4ply arena)
-------------- -------------- -------- --------------- --------------
1 acct, sequential 4795 0 extra 48 min 480 min
1 acct, smart 4640 0 extra 46 min 460 min
multi, sequential 3280 192 extra 71 min 368 min
When using the gem trade glitch single account is clearly best as the extra price (at 100 gems/min) are still much less than the equivalent time to transfer the 192 heads to your main, however if you desire to earn the gems via non-glitch means, the chief consideration is price, and the multi account method is preferred. This holds even more so for regular arena or progression-based modes of earning the gems.