Load up chapter 6-2 Breakout
For the purpose of this solution, reading that it said "Rescue your brother without killing him" I wondered would it pop if I died? So purposely I killed myself but made sure the brother never died and once I got to the end..... CHEEVO!. So I can confirm that you can die but the brother can't, which makes this the easiest of the no death achievements.
Just take your time as there is no race against anything to cause you to make a mistake under pressure and you should get this with very few reloads, if you do kill him then just hit start and restart chapter, this will reset it and won't void the achievement, do not go to restart from last checkpoint as it won't count
Here's a video showing how it's done, which isn't made by me so credit whoever posted it