This is not a normal solution but the way I got it. Maybe it will unlock for you in the same way, so here it goes.
I first completed the entire game on casual with the starter dragon (upgraded and evolved, of course). This means every mission in the game completed. After that was done, I went back to my base and changed the difficulty to classic. Used the same dragon and also a wingman to play the very first training mission. Got an 'A' with over 90.000 points and unlocked this achievement.
Since every mission still has a mission rank attached to it, the game might think I beat every mission on classic instead of casual. So just beat every mission on casual, change to classic and beat the very first training mission (super easy).
Not sure if this will work for everyone but I would at least try it this way.