Best tips for placing high in arena assault

AA is the same with arena, you need +40 merges unit, and if possible a legendary blessing for higher score.
normally +20 legendary hero and +20 blessed armor or a +10 legendary hero and +30 blessed armor hero can score high.
also the scoring is on your first battle, so 6 battles after that is not score relevant anymore afaik.

Check out the Gamepress guide:
https://fireemblem.gamepress.gg/arena-assault-scoring-guide
There is some detail about blessings, such as blessed units during the active season on the 6 subsequent teams (after the first scoring team) add 1 point to the total score each. That is poorly worded; just check the guide out.

Use slaying hammers, use armoursmasher, use Falchion and other anti-dragon stuff, use bows, use breakers, use TA and gem weapons, use healers and dancers wisely with impunity, and don't forget positioning assists.
Have enemy phase units in case they have a strong team with a dancer.
If you have issues with Veronica, Micaiah is quite good. She'll tank two hits with her strong res and she can OHKO with death blow despite all the stolen stats.

Basically, hard-counter the stuff you see in your scoring range because you know exactly what's coming
Bold fighter breaks down when it runs into a breaker who isn't slow enough to get natural doubled
Reinhardt loses to TA green mages
B.Lyn gets busted by bowbreaker
Etc.