Enigmo is unique in the puzzler genre because it does not let you select individual levels to play, even after beating them. You start at Level 1 and progress linearly through the game, saving your progress and moving on after completing the last level.
Just start at the beginning and progress through all the levels. You should be using a guide for each level as that will give you the most score in the least amount of time in order to work towards the "Respectable" and "Enigmaster" achievements. Follow the guides below.
Thanks to YouTube user SullyTheFatDude for the videos!