When I saw the list I thought the online trophies will be time consuming, but apparently the game has crossplay with all other versions including the mobile game. I downloaded it for free off apple's app store on my iphone and was able to matchmake with myself on PS. It seems that the game is also available for free on google store. Now, since the game is free on mobile, you will be interrupted with a short ad between each match that can cause you to disconnect before the rematch prompt. Also, you can decide the settings of your online match which makes the online trophies way faster to achieve. I experimented with different settings and found which are most time efficient. Here's a quick step by step guide:
1) on PS version, go to "Create Room". You will be given a room code to share. On the mobile version, press "Join Room" and type up that same code from the PS version. You will be prompted to pick a team on both version. Pick anyone, it doesn't matter and hit continue.
2) Now on the match settings screen. On both versions, put "Score Max" as 1 and go to modifier settings and change "Sleepy Keeper" to ON. Leave all other settings the same. This ensures that the game automatically ends when any player gets one goal. You want to make sure that you do that on both versions because the game will otherwise pick one of the two choices at random. Hit continue to start the game.
3) Once started, on PS version pick up the ball and score one goal against a sleeping keeper, and the game should end, giving you a win on the PS version.
4) Now the annoying part about the ads. You will be prompted to a score page on PS, while the mobile version will start an ad. Don't press anything on the PS version at this time and wait on the score screen while the ad finishes playing on your phone. Once both versions are on the score screen, press "Continue" on both versions then "Rematch". A new game should starts very quickly. If you accidentally hit continue on PS version before the ad ends, and the game disconnects, start over from step 1. This is not that time consuming honestly, but I found it annoying to have to retype the room code and go through settings every time.
5) Repeat 99 more times.