This is by far a hard achievement to unlock, and requires a constant presence of Noodle's full body, which is hard as most of it is off screen. My biggest tip for the achievement will be to take your time. Don't rush a spot unless you know 100% you can do that spot without there being an error. The big tips are to use
for Doodle to hold onto your tail and
for Noodle to grip onto the surface he is currently climbing.
*On a side note before going through everything, if at any point you think the tail may have hit the water, or you know for sure it did, I would quit out of the level and select it again from level select.Overall, there are 7 main bodies of water that you have to avoid. The first one is easy to avoid, as you just have to go to the left. Have Doodle lift your tail up, just in case, and make your way onto the bridge. From the bridge, go to the bit of land and climb the wall there. Again have Doodle hold your tail up and once you get to the top, you are safe to drop it and make your way to the Green Keystone.
After the Green Keystone, you will want to drop down and get ready to cross the Bamboo, but be sure Doodle is holding your tail, as this is a spot that the tail will nick the water, then cross over and go to the right after the checkpoint to avoid the water spot 4. You can climb on the wall, and once you get up there, you are safe from water until after the Red Keystone.
After the Red Keystone, take the first slide down as normal, but for the second one, you will climb over and jump down. Be sure, once again, that Doodle is holding your tail. The reason you jump down and skip the slide is that the slide will put you in the water. Follow the ledge and go up to the turn wheel, and once it is completed, make your way back towards the slide and then follow it up to the next checkpoint. Cross the new bridge, I would recommend taking your time, but my method has worked, as long as your timing and speed are on par. Continue to the Bamboo to climb up to the top area and get ready for the hardest part.
Take your time here, as getting the Yellow Keystone is a pain, and we don't want our hard work to be jeopardized by a foolish mistake. Be sure you continually wrap yourself around at the different points, as that will help keep you up and not fall into the spikes. Once you get to the end with the Yellow Keystone, wrap yourself a few times, just to be on the safe side, as Doodle will drop your tail, which in turn can fall into the water.
After the Yellow Keystone, have Doodle, once again, grab onto your tail, and jump off to the left towards the little bridge path that goes down towards the end. And here we are, the final jump, be sure that you jump far enough, and that your tail is being held by Doodle. When you make the jump, you land close enough where Doodle will drop the tail and put the Keystones into there place. With this, Doodle drops the tail around your head, keeping the length of the snake half of what it normally would be. After the cutscene, don't move until Doodle grabs the tail, and go into the portal and the achievement should pop.
Hope this helped, and if you have any questions, feel free to ask and I will do my best to explain it.