In Brain Quiz, the main goal is to score as many points as possible within the span of twelve minigame cards.
"Oops! All BQS" is all about how many points you can score with a limited set of minigames, or more specifically, with the five minigames that only ever make appearances in BBAWD's Brain Quiz mode: Tick-Tock Turn, True View, Frame Filler, Order Out, and Pattern Puzzle. Getting multiple True View cards is highly recommended for this type of run, and lucky for me, I got three of them. The bad news is that two of them were EZ, which doesn't score that many points and the good news is the last one was an MDx2, which scores far more points than HD if played optimally. This isn't shown in the YouTube video, but I start off the Brain Quiz by exiting and entering the game again hoping to get a better set of cards. I did this until I made sure that I got an All BQS set with three True View cards. I ended up having to scrap and restart the run several times to do this in a reasonable amount of playtime.
I have timestampped each minigame in the video, along with the scores from them. Also in the description is a Google Sheets I made that shows all individual Brain Quiz TAS WRs from this TAS, my (now obsolete) previous TAS, and sock puppet's 644 points TAS.