I had quite some problems to destroy some of the locks because I had my character so well skilled in lockpicking. Missing the obvious, I started to despair with enormous amounts of quickloads.
The obvious thing to do is just to put 1 skill point to any chracter who is not skilled in locklicking. With this single skillpoint you will most often find a 10-18% chance to lockpick something. You will get a critical failure in no time. Use the same character as your mechanics expert to save some time. I had 5 points spent to mechanics on the same character when I unlocked the achievement.
The tactics mentioned in the other solution (always quicksave/quickload) is essential for this to work without much of a hassle.
All in all I got the achievement when I was about to enter the prison area, rather early in the game.
Hope this helps you guys.
Any improvements? Please let me know in the comments below!