RetroAchievements
7.9#1 in game achievement trackersFree planFree planAndroidiOSWebAPI
VisitNo prices published.
RetroAchievements suits players who want achievement tracking, profiles, and friendly competition while playing supported retro games through compatible emulators. It also has options for developers using its public API and players willing to start sessions online.
You want what its maker publishes above — check its page for the details.