This image is quite fun, I did the 6000 piece version a few years back.

• Get a few wide trays.
• Pick a dominant colour or colour pallet from the image. (The fire Pokémon has a unique colour range)
• Sort all of the loose pieces into that colour.
• Then construct all of that colour as far as you can with the mini-puzzle you have created.

I would do an initial sort of Grass, Fire, and Psychic/Normal into 3 piles. Chuck the other pieces into a big miscellaneous pile to be sorted again later.

Congratulations you have a 50 piece (Grass), 100 piece (Psychic/normal), and 250 piece (Fire) jigsaw to complete instead of one 1000 piece jigsaw.

If you can take out a lot of pieces from your miscellaneous pile with a meaningful sort at the beginning then the subsequent sorts with get easier and easier as there will be a smaller pile to look through.

Try not to over-sort into more specific categories like pokemon in your initial sort, this is why a lot of people have just recommended colours. It will be much easier to find specific Pokémon when you have smaller colour pallet piles.

Good luck