You have to get to rank 26 by getting 240 stamps for this achievement. This seems daunting but is very doable. Just keep plugging away at it a few challenges at a time.
There are 10 stamps per 2d retro game included in the game consisting of 5 for achievements for playing the full game and 5 more for the snapshots. Each snapshot playlist will net you 5 stamps once you complete it. Skip the ones you feel like you'll have the most difficulty getting until the end so you can pick and choose. A lot of them are pretty easy or just grindy. The retro games are definitely janky, but the rewind and other cheats make the regular stamps mostly a minor annoyance. There are plenty of videos and guides out there to help with the more tricky ones.
The N64/Xbox retro games each have 12 achievements which give you a stamp per achievement. These are more of a time sink, but also more fun in general. Of these, Conker's Bad Fur Day is the easiest/quickest to get all the achievements due to scene skip cheats.
For the 360 games that have their own achievement lists outside the collection, 75% achievement completion nets you the full amount of stamps for each one. Be warned that some of the older of these have pretty crummy or difficult achievement lists.
Focus on what you enjoy and can do easily, and then mop up the rest over time. This took me a while, but I kept going back to the game to complete a few stamps each time, and I eventually got there. This is absolutely doable.