The Batman Arkham Trilogy reviews are starting to come in for the Switch and it sounds like the performance results are mixed.
Batman: Arkham Knight is a game that has had issues on other platforms, but as it stands right now, barring a patch, it’s the worst performing game of this trilogy on the Switch by far. Batman: Arkham Asylum and Arkham City seem to be somewhat better, mostly maintaining a 30 FPS framerate in handheld mode and dropping pretty frequently in docked mode. Not great, but playable.
All three games downloaded to the Switch come in at around 45 GB, so a SD card will be necessary. Even the physical version of the game only comes with Arkham Asylum on the card, so a hefty download will still be required. Who knows if WB Games will bother with any future patches for this collection, but it might be worth waiting to see if they do.