If you're the cautious type, and I know I am, you might have taken one look at the words "Timed Challenge" and just gone "Nope". Well, in actual fact, you should be trying to play this mode ANY TIME YOU PLAY A GAME. (Well, except maybe your first time so you can get a feel for how long the game is.) As near as I can tell, the only differences between Timed Challenge and Normal Play are: a timer added, the save/load feature getting disabled (okay, that one might be rough for folks who need it), and (most importantly) a bunch of bonuses get enabled for how many CASPO you get per play. A LOT of bonuses.

You're not fighting a Time Limit. You don't need to beat a bunch of professional speedrunners to get a high rank in order to get any worthwhile amount of points. You can use Rewind as much as you want. You just need to beat a game in Timed Challenge mode. There's possibly one or two games where it's less simple, but even then you could probably just wait for when the revolving bonus points of the week line up with that game in order to get enough of a further bonus to break 50k CASPO.

This cheevo should not be rare. This cheevo is a gimme.

(That said, if you do find a game where clearing it on Timed Challenge isn't enough, post a comment about it so others don't waste their time on that game. I didn't test all the games' Timed Challenge and I'm not about to play Vulgus again to find out.)

Edit: Don't forget to watch the Intros, Credits, and other parts that get cut from the Timed Mode versions of the game if you opt to not play Normal Mode. These games are art and you should experience all they have to offer. (Thanks to sumolagann for the reminder!)