Ripper Roo will follow an exact pattern for each piece of his life. To take his life bar away you must jump on a TNT crate and have it explode while beside Ripper Roo. Since he follows an exact pattern there will be what I refer to as a safe zone you can stand on.
Life 1 - Ripper Roo's pattern will be middle center, bottom left, middle center, bottom right and then back to middle center. Then his pattern will recycle back and forth until you hurt him the 1st time. Your safe zone is middle left. You want to hit the left TNT when it is in the middle and Ripper Roo is on the bottom right platform. You want to escape from the dynamite and go to your next safe zone which will be top right.
Life 2 - Ripper Roo's Pattern will be middle left, bottom center, middle right, middle center, and back to middle left. Then his pattern will recycle until you take his second piece of life away. Your safe zone will be top right. When the right TNT comes downstream to the middle wait until Ripper Roo is middle right. As he jumps to middle center time your jump and jump to middle right and hit the TNT right away as Ripper Roo is on the middle left. Make your escape to your next safe zone which is top left.
Life 3 - Ripper Roo's Pattern is bottom center, middle left, top center, middle right, and back to bottom center. Then his pattern will recycle until you take his final piece of life. Your safe zone is top left. When the left TNT is at the top you want to jump on it as Ripper Roo is leaving the top center platform. Make your escape to the top right platform while the TNT explodes.