Tips to increase your score:

1. Use four 5* units at level 40.
2. Use units with maximum merges.
3. Use maximum SP skills.
4. Use a bonus unit (preferably a bonus legendary).
5. Use up to 2 legendaries of the same in-season element.
6. Bless all your non-legendary units with the element of those legendaries.

Choose units with the highest BST or legendary/duo units with the highest "Duel" effect. You can find a tierlist of the best scoring units here.

Complete formulae to calculate score.