This method does not use save editing or glitches!!!
Is it still cheating? That's debatable!!!





It's simple, even if just a little bit tedious.
Before I actually get into the method, though, a bit of advice.

• If you don't already know how the quicksave works, try it a few times. The most important thing to know is that loading one respawns you at the last checkpoint you touched, so you can't save in the middle of a room and continue from there after quitting.
  
• Get at least one S or V rank on the time trials. This will help you figure out what the least risky ways of clearing certain rooms in the game are.
  
• Don't go out of your way to grab trinkets. I don't think I have to explain this one.
  
• You can check how many times you have died so far by pressing the pause button (usually enter on keyboard, I don't know the keybind on gamepad, sorry) and scrolling over to stats in the menu.

After you start a new game, play normally until you have made it to an obstacle that has a solid chance of killing you (e.x. Gantry and Dolly, Stop and Reflect, Driller). Make a quicksave and attempt to cross the obstacle. If you fail, reload the quicksave and keep attempting and reloading until you make it. Apply this to any room in the game, and you can easily make it through without the game thinking you've ever died.

The Gravitron sucks.
You can't save during it in a way that really matters, either.
Fortunately, we are not going for a perfect run, just one that's good enough to get our achievement. This means that as long as we don't surpass our threshold of deaths, we can die as many times as we want here. I'd recommend to keep running The Gravitron and checking your deaths afterwards, reloading your save if you made too many mistakes.
You can also use this strategy for other rooms you find challenging, but don't do it too often or you may make it harder on yourself later.

After you complete VVVVVV and see the Game Complete screen, you should have gotten the achievements; you can confirm by checking the secret lab or Steam.

Congrats! You did it!