Garnet/Sapphire Sanctum Achievements
It doesn’t matter if you fall, as long as you get both halves of the key and open the chest. Make sure you’re doing it on different maps, though! There are three different WvW Borderlands maps – each of them have the same jump puzzle in the same location, but each unlocks a different achievement (Emerald/Garnet/Sapphire) for completing the puzzle in that specific map. So you’ll have to do it three times, once per map, to get all three Sanctum achievements.
If you’re not getting the achievement for finishing it in that map, you’ll probably have to try the other Borderlands.
Keep in mind that the sanctums are based on the color. So while you were green last time (and got emerald sanctum) you will need to travel to the borderlands of the red and blue worlds to get the achievement. (even if it’s your own world again)
Also, as far as I aware, it doesn’t matter where you get the key parts. You just need to have them in inventory and then you can go unlock whatever vault you didn’t open before.
Also: Garnet = Red, Sapphire = Blue, Emerald = Green. I don’t think the general player population (myself included) knows this by heart.