To earn the He’d Be So Proud of You achievement/trophy in Gotham Knights, you must “Reach the maximum level as any member of the Batman Family”.
To earn this achievement you’ll need to reach level 40 with any one character. Since all characters level up simultaneously, you don’t need to worry about who you’re playing at any given time - if you’re earning XP, you’re making progress. That said, you can only reach level 30 on your first playthrough, and even this will take some grinding, followed by more XP grinding on New Game+ to go from level 30 to 40.
There are many ways of earning XP: defeating criminals, stopping crimes, completing challenges, but arguably the best way to earn XP in both your first playthrough and in New Game+ is by simply completing case files (both main quests and side quests) and completing training/tutorial challenges in the Belfry. At higher levels you can expect to gain tens of thousands of XP from both case files and training challenges. Replaying the training challenges earned us a few levels, and on top of that we had to play through the main case files until we reached Case 04 to finally reach level 40.
Given that you can’t surpass level 30 until you start New Game+, this very well may be the last achievement you unlock, depending on how much you accomplished on your first playthrough. If you have to clean up other trophies on New Game+, you may have to advance through the main case files significantly anyways, in which case you’ll likely earn this achievement as a byproduct.