I've found what I consider to be the absolute fastest way to do this, possibly as low as 30 seconds or less, and you don't need a solver or a screenshot. You can do everything in-game. Use the guide on the left, third button down. It'll actually take a few seconds to turn that on and press the first number... and you'll STILL get your times way down.
When the guide is turned on, all of the possible spots that a number can go are automatically highlighted. It'll be obvious which ones are the actual places to put a number. The more you do it, the faster you'll get.
In this one, I've hit the guide button and then 1 at the bottom. Those squares are highlighted. Note the circled one is the only one in the row. A 1 goes there. A second 1 goes in the first column, 6th row, then after that row is cleared, 8th column, 5th row, and so forth. Follow it through the board, and when you can't find any other obvious spaces, move to 2, then down the list.
(Not the same puzzle) ...and that wasn't even my best time. I got 0:25 on Number Puzzle.
Expert will take longer, and even then my best time was 1:12. So this can go very quickly without the need to go outside for a solver, and the game has the helper built in.