Rogue Galleon is a very simple game. You kill enemies, collect coins, unlock characters and weapons, and purchase upgrades. All of the achievements are self explanatory except for one which requires a little finesse.
It's recommended that you unlock the gold storage upgrade and unlock the upgrades for the roll before attempting this achievement. You might want to leave this achievement for last as it would make it easier.

In the settings there's an option to roll in the direction of your cursor. Enable it in order to make this achievement and your experience a lot smoother. Then you'll want to select a character other than the Saboteur, Juggernaut or Rebel as per the achievement.
Use your roll to knock enemies into the walls, and eventually you'll make it to room 5 and get the achievement. The upgrades for contact damage on hitting enemies with the roll and for longer invincibility when rolling make this achievement much easier, however you start without any upgrades. It's up to your luck whether you get these upgrades after the first room or at all. Resetting to get them and make your time easier is viable.
The achievement should unlock once you reach room 5, so you shouldn't have to complete but 4 rooms.