The goal was to run Abbot as fast as possible with the minimum number of players possible, two. Two people are needed to completed the tiles puzzle, and (realistically) to get the other person out of encase, whereas other elements of the raid can be soloed. This is not a speedrun in the full group sense, where it's the minimum amount of time possible (usually indicating a full group), but a speedrun in the minimum amount of time possible given the constraint of using only two people.
As a speedrun, the main challenge for this raid is to be able to do all the puzzles in one round, so that the raid isn't unduly delayed by having to beat down the Abbot multiple times (other than the initial fight). The asteroids puzzle is timed, so a player that gets into asteroids is effectively locked in there for the rest of the puzzles phase of the raid, since it lasts for 200 seconds while the dimension doors only stay up for 90 seconds. This means that the other two puzzles -- tiles and ice -- should ideally both be completed within the 90 seconds that the dimension doors are up, and then the players both go do asteroids together and do the puzzle while waiting for the Abbot to come down.
In reality, we don't know what the order of puzzles will be. So there are a few "abort" conditions, mainly if a player gets locked into asteroids too early and thus it becomes impossible to complete the puzzles in one round. Those possibilities were:
first puzzle = asteroids -> abort (impossible to complete tiles)
first puzzle = ice, second puzzle = asteroids -> abort (impossible to complete tiles)
This means that the remaining order of puzzles need to be done in one round:
first puzzle = ice, second puzzle = tiles, third puzzle = asteroids
first puzzle = tiles, second puzzle = ice, third puzzle = asteroids
first puzzle = tiles, second puzzle = asteroids, third puzzle = ice
For the third possibility here, if the second puzzle is asteroids, then there are two options: either that player solos asteroids (which is perfectly doable, I've done it plenty of times), or the other player, hearing that the second puzzle is asteroids, goes into the remaining puzzle, ice, solos it (which is also doable), and then goes into asteroids before the dimension doors go in, which makes asteroids easier since there'll be two people for the majority of it, but is a lot more difficult time-wise. Otherwise the third possibility here also becomes an abort if this cannot be achieved. Because we wanted to minimize the number of resets, however, we worked on being able to handle any of those three possibilities.
For this particular run we were just practicing, so weren't really intent on completing it at the outset. However halfway through we were like whatever and got bored of practicing so decided to just finish. I was hoping for a flawless run but I died at the very end with the Abbot at 3%. Also, my ship buffs ran out halfway through (obviously I wasn't paying attention) so toward the end I was effectively not buffed and didn't have resists, not to mention disjunctioned, leading to the death. In any case the next time should be a flawless run and likely faster. Some screenshots:
In this particular run, tiles and ice combined took a total of about 75 seconds, so there was a 15-second window between when we went into asteroids and when the dimension doors went down. Because Abbot is now at 135k HP, and we need to take him down to 2/3 of his HP in the initial fight, we effectively need to take out 180k HP. Given that the puzzles take around 6 minutes, this means that it took us a total of around 9 minutes to take him down, so the DPS was effectively 180k/9/60 = 333 or so throughout the non-puzzle part of the raid. This is largely due to stuff like inferno and encase, so can certainly be improved upon in future runs.