Just playhrough the game and you'll see ...

1. It doesn't matter if you are wrong guessing you just need to right guess 2-3 times in a level to proceed

2. With each of the higher levels your chances to right guess becomes lower
Egypt 2 cards (50%)
Maya 3 cards (33%)
China 4 cards (25%)
Greek 5 cards (20%)
Nordic 6 cards (16.6%)

3. Playthrough only once to get all basic achievements

To get the rest of the right guess (numbers) achievements you are supposed to play
only the Egyptian level. (50% chance of right guessing)

If game asks you to proceed to next level just answer "continue" and you'll
stay in this mode forever

Never think you are a Psi genius. The cards are random and
if you pick the wrong one nothing is left ... except to pick also the other one.

Sure your Psi chain will break after this but you'll get the achievement in either way.

So if you see this:


Click first the left card. If no achievement pops quickly also click the right card:

After doing this 444 times you finally have become the Psi Expert.