Survival mode is initially locked at the start of the game.
In order to unlock Survival mode, you must finish all 4 of the Shows on Easy difficulty.
Once available, Survival mode plays through each of the 20 blueprints, and then loops over and over with increasing difficulty. The blueprints are the same as in the Shows, but you only have one life. Once you lose, you are kicked back to the menu.
To unlock the achievement, just play through the first 20 blueprints without failing. Since you should have already played all the blueprints at least once in the Shows, this shouldn't be much of a challenge.
If you need practice on any certain blueprint, use the training area.