When I checked the Monthly Achievements the other day, I was at first very put off due to the 30 Jumping Puzzles it seemed I would be doing. I know some people like those, but I personally cannot stand them and avoid them at all costs. Figuring I would just get it over with, Pyanfar and I decided to spend some time and get it done.
A very frustrating hour later, we discovered that to get this achievement, you simply have to 'Discover' the puzzle, which only requires your physical presence at the BEGINNING of the puzzle; you do not actually have to COMPLETE or even attempt it. This lead to a bit of testing, and now I will share this with all of you:
* As stated, simply need to hit the entrance, no need to complete.
* This is recorded on a "Per Character" basis, meaning you can use your alts to get credit from the same puzzle.
* Did not test this as I have no spare character slots, but I am pretty sure you can create an alt, discover a Puzzle, delete it, recreate, rinse and repeat.
* Lion's Arch has 3 puzzles that anyone can very simply discover. Do this with 8 characters if you have one of each like me, or use the Reroll method to make alts over and over, port to Mists, then to LA. Each alt nets you 3 Discoveries.
I did do the puzzles as I was already there, and I found them to be fun (some of them at least) but if you really want to just get it out of the way, this is how. Hope it helps!