What's the average score needed to reach t20?

If you want to get into 19.5, around 706-710 or something like that.

706 per match is borderline and chance of not making the cut. It’s always slightly increasing as well.

https://fireemblem.gamepress.gg/node/372796

I score 706+ (more if there is earth blessing active), and i bounce between 19-20 tier every week.

Last week my score was 3,606 and I dropped back down to tier 19. I average 714-724 score range it seems. To stay in 20, seems like you may need to be getting 720+ every single time to have a shot at it or spend a bunch of dueling swords and only fight if you get 724+. If you just want to get in to 19.5, you should be able to do that with ~710 matchups.