heh, I am not a 4 player try hard (there's nothing wrong with em)
Simple mates with fairy pieces

If you include positions that include a royal piece other than a king, then there are legal moves, in which a royal king checkmates a royal knight, but the royal knight must cooperate, in order to get checkmated, and the royal knight can never checkmate the king, meaning there are no forced checkmates. https://www.chess.com/4-player-chess?g=3761438-100
A royal king can force checkmate against a royal wazir. https://www.chess.com/4-player-chess?g=3761543
Bishop in Camel Forest: https://www.chess.com/4-player-chess?g=3761616 Both kings are forced to move only diagonally, meaning that a king and bishop can force a checkmate.
2 Dabbaba-Riders in Camel Forest: https://www.chess.com/4-player-chess?g=3761690 The comfuter did cooperate a bit, but even if it didn't the way the king is forced to only move diagonally means that the Dabbaba-Riders can force a checkmate.

Thank you for posting!!! Also @Tacticspotter I considered doing grasshoppers but it would take like 10 of them so no

Actually I didn't know that it is possible, to play 4-player chess with Fairy pieces on chess.com. How can I start such a game?

@everet823 fairy pieces were recently added to 4-player chess on chess.com, and you can play with fairy pieces by going to the edit position, and clicking on the picture of a knight with a king on it. I was actually the one to suggest adding fairy pieces, although some other members suggested some of the fairy pieces.

Is there a manual? I have no clue how to come to 'edit the position' and there is no picture of a knight with a king on it. Is it when you already have started a game?? Can you otherwise explain this step by step?
Thank you for posting!!! Also @Tacticspotter I considered doing grasshoppers but it would take like 10 of them so no
that's what I expected and that's why I'm too lazy to do it

This is an example game, in which I used 16 grasshoppers to checkmate the comfuter.
https://www.chess.com/4-player-chess?g=3779329-59

https://www.chess.com/4-player-chess?g=3779892 In this chaturanga game I checkmated 2 comfuters and one dead king with a dabbaba and a Wazir. Like 2 Alibabas, this combination of pieces forces mate when in the right corner, but it is not possible to force the opposing king into the right corner unless they cooperate. The right corner is the corner that the dabbaba can control.
To practice elementary checkmating with fairy pieces, you can use this applet. You can even specify pieces of your own design there. It always uses an orthodox King, though. It works by means of constructing the End-Game Table, so it plays perfectly.
I see that the 4-player board is larger, but since the central area is also 8x8, I expect there isn't much difference in technique; if you are able to drive the bare King into a corner of a plain 8x8, it must be possible to drive it out of the central 8x8 area as well. And once in one of the side panels, it is like being on 8x8 all over again.
If there is interest, I could also set up a version for the 4-player board. I was thinking about supporting larger rectangular boards anyway. For 3-men end-games the size of the table is not yet a problem even on 16x16 boards.
Btw, on 8x8 4 Grasshoppers is enough to checkmate, and for the above reasons I would expect it to be sufficient on the 4-player board as well. A 2x2 swarm of Grasshoppers interdicts access to a 4x4 area, acting as a sort of super King, and can still still easily extend its interdiction area sideway by converting to a diamond shape. So it can form an inpenetrable confinement wall along a rank 6 files wide, and you can close off 3 more files with the King. Should be very easy.
You are probably thinking, "I know simple mates, they are easy! You can mate with Q and R and BB and BN but with nothing else." This is true, but with 20 different fairy pieces and a non-royal king, there are a lot more simple mates to analyze. Here are a few basic ones I did against a comfuter and the result:
Amazon: https://www.chess.com/4-player-chess?g=3757707 Easy Mate
Elephant: https://www.chess.com/4-player-chess?g=3757714 Easy Mate
Hawk: https://www.chess.com/4-player-chess?g=3757729 Mate
General: https://www.chess.com/4-player-chess?g=3757740 Mate
Wildebeest: https://www.chess.com/4-player-chess?g=3757754 No mate, unless the opponent blunders
2 Ferzes: https://www.chess.com/4-player-chess?g=3757802 No mate, unless the opponent blunders
2 Wazirs: https://www.chess.com/4-player-chess?g=3757833 No mate, unless the opponent blunders
Knight-Rider: https://www.chess.com/4-player-chess?g=3757870 Mate impossible
Camel-Rider: https://www.chess.com/4-player-chess?g=3757886 Mate impossible
Alibaba-Rider: https://www.chess.com/4-player-chess?g=3757907 Mate impossible
2 Alfils: https://www.chess.com/4-player-chess?g=3757916 No mate, unless the opponent blunders (note: the mate with 2 Dabbabas is not covered because it is very similar to 2 Alfils.)
2 Alibabas: https://www.chess.com/4-player-chess?g=3757945 I am very on the fence about this; the result of the game was that this is a very hard but possible mate without stupidity from the opponent, but I would appreciate a post confirming or rejecting this hypothesis.
2 Camels: https://www.chess.com/4-player-chess?g=3757962 No mate, unless the opponent blunders
Finally, I know that the king is not a fairy piece, but you probably have not learned how to mate with 1 royal and 1 non-royal king because normal chess does not have promotion to kings. So:
King: https://www.chess.com/4-player-chess?g=3758006 Mate
Post if you got a different result in a game or if you want to add a different basic mate. Here are the rules for new basic mates:
1. Let's call the set of all your pieces in the mate P. If it has been proven possible that a subset of P can also be used to mate, your mate has redundant pieces and therefore should not be posted.
2. Easy mate < 15 moves, very hard mate requires a lot of thought or takes close to 50 moves. Anything in between is just mate.
3. If you achieve mate, check to see if the opponent could have escaped mate easily somewhere during the game (especially if you are playing against a comfuter or a randobot).