For this achievement you simply need to unlock the last gate and open the final chest in a single map on Adventure mode. You'll have to get at least one star in all of the normal (i.e. not bonus) levels on the map. There are 80 such levels in total. Additionally, you'll need to have 156 stars from the levels on the map to unlock the final gate. The game displays how many stars you have on the map at the top of the screen. I've found the best way to quickly work through the levels is to go after the objectives that relate to the special tiles in each level. You usually only need 2-3 words to finish the objective, so they go fast. If you need to get more stars to unlock the last gate or any of the ones preceding it, usually the earlier levels have easier objectives than the later ones, so you can get three stars more quickly on those levels.