For the "Freedom Hero" achievement (free all Gift Shop prisoners by unlocking or trading), do I need to seek out other players for trades, or can I theoretically get enough gems in one game to buy everyone by myself? Are there any specific prisoners/heads/masks/hats that will not unlock in my game by any means (like Fable 3)?
If I am interpreting your question properly, yes and no. :D
Let's say you play through the story mode. The total gems you can earn by playing through single-player and co-op on both normal and insane mode for both and you get A++ on every single level (encore levels included) you will NOT earn enough gems to buy every single head (I know because I did it myself, I was ~300 or so gems short).
That said, you can earn gems playing the VS online modes. If you don't know already, you get 2 gems for losing a match, 4 for winning a match and a potential 1 gem for MVP (which can go to anyone regardless of win or lose, it's just based on who the game determines is "best"). So for each match there is a potential for 5 gems to be earned.
So you can gain the remainder of the gems via the VS mode, or you can trade with other players if you so choose. On the matter of the achievement itself, you only have to acquire all heads in each of the 4 "standard" head categories: circle, square, triangle and cylinder. The star heads have no count whatsoever towards the achievement. Also, the game only checks that you have all of those given heads with you at any one time (you don't actually have to purchase every single one from the gift shop).
I just acquired this achievement last night (and 100% the achievements for the game in doing so. WOOT!) so I can confirm all that stuff. I actually had someone trade to me the remainder of the heads I needed and I just got the achievement.
Hopefully that answers your question.
On a side note, I realized that you can technically earn the extra gems on a separate profile (local if you want even) and trade either the gems to your main profile or buy the heads and trade those over. So you could play through the entire game twice (or as many times as you want I suppose) on more than one profile and just trade over all the stuff you need inside a local co-op game. Anyway, just an extra little tid-bit there. :)
Yes* you can, and the achievement says it all by itself
"by unlocking OR trading" and not
"by unlocking AND trading".
After unlocking every prisoner in the Gift Shop you will get the achievement.
*This however is only for the prisoners in the Gift Shop.
The Star Head prisoners
can't be purchased at the Gift Shop, they are special unlocks that are available after completing certain tasks.
They are available for a limited time, although The Behemoth has stated in a Blog PostingHere
that the Special Star Prisoners will come again sometime in the future.
You can see further information on how to get some of them here.