In 13x13, there is not much useful in the centre. This is for both players!
Beware of following your opponent around - in particular, if they’re doing endgame-type things, ask yourself if there is something bigger you could be looking at.
(Related) play consistently - if you make a move with a purpose and your opponent doesn’t respond the way you thought they might, then think carefully before you agree with them. Maybe they’re wrong. Actually there’s a huge moment in the game where your opponent makes this mistake too
Shapes.
4.1 Look up the common broken shapes (broken keima, broken tobi, elephant’s eye, etc) and read them before you play them.
4.2 Watch out for the dreaded empty triangle. Both players played several, and I think only one of them looked like it was right.