Win one great league trainer battle against another trainer in Pokémon Go is a confusing task that popped up today on players' games. The task had a bug that was quickly fixed, but it isn't obvious how to get the task working.
Win One Great League Battle Against Another Trainer Pokémon Go: How to Fix Task Glitch
The original task would not be marked as complete when you actually did win a Pokémon battle. Niantic has updated the task so you can complete it by winning any battle with a trainer.
Only future task that are assigned will have the fix, so if it's not getting done you'll have to get rid of it and reacquire the task.
Once you have the updated task, you can easily complete it without meeting anyone physically, as Niantic has lowered the requirements to partake in Trainer battles amid the global COVID-19 quarantines.
You can battle with Good or Great friends, and Niantic has removed the step requirement previously needed to unlock battle sets.