In order to obtain all the achievements you will need to:

• Complete all the levels
  
• Complete 15 levels in less than 15 seconds - this should be easily obtainable, even without a guide nearby
  
• Complete 25 levels in less than 10 steps each - most of the levels can be solved in under 10 steps; however, while figuring out a solution, it happens that the same steps are repeated over and over again, thus increasing the total number of moves.

While solving the levels, there will be no need to click a square more than once. The squares that end up being clicked twice can be completely removed from the solution.

Also, the order in which the squares are clicked does not matter; the numbers listed on the screenshots are just indicators for the total number of steps.