Recap of the rules
You're given a grid of 16 words that have to be split into 4 sets of 4, each with a defining theme. For example, in today's puzzle, four of the words are 'iguana', 'monitor', 'gecko', and 'chameleon', with the theme being 'lizards'.
On the first guess, you pick 4 of the 16 words. If these words form a set, they are removed from the pool and the game continues with 12 words. After a second correct guess, the pool is 8 words, and so on. If they don't form a set, the game counts this as a mistake. You can make 3 mistakes and continue playing, but a 4th mistake ends the game.
One more note about mistakes. If your guess contains 3 words from one set and 1 word from another, the game will still count it as a mistake, but will also give you the hint 'One away...'.
Puzzle
The question is this. Imagine you've made two correct guesses, and the board now contains 8 words that need to be divided into 2 sets, but you have no idea what the connections are. From the additional hint, and the fact that there's only two sets left, you can tell if your guesses are correct, one off, or two from each set. Is there a strategy which guarantees you win?
If not, how many guesses would be necessary? An absolute upper bound would be ${8 \choose 4}=70$ but that doesn't take into account the extra hints.
(To be upfront, I don't know the answer. Hoping the smarter people here can help.)