Difficulty chievos stack.
But... maybe you should concern not to try Impossible difficulty first when you're new to the game.
Anyway - as the guide says, you need 5 playthroughs for another chievo anyway, so I suggest 1 or 2 normal or classic playthroughs to get into the game and mop up some of the achievements before you try Classic ironman and then Impossible
Ironman mode and especially Impossible difficulty are very unforgiving and frustrating and when you start with those... well, you may learn to hate the game very fast
(I started on Steam back at release days and with Impossible Ironman and I needed like 35 tries to even finish the first mission with no one killed - so never play Imp/Ironman!