What are your tips on improving your APFT score?

I can tell you what I used to do with one my squads and it works wonders. Our squad had one of the highest average scores as a squad in the battalion.
Monday - PT test
Tuesday - Swim laps for 10 min, push-ups, sit-ups
Wednesday - Run
Thursday - Swim laps for 20 min, nothing else
Friday - PT test
Squad average - 294
My highest 308 (and I wasn't the highest in the squad)

Interval training worked well for me. 300 x 2

There are multiple ways of "Training for the Test" (which isn't necessarily a good mindset, but that's another discussion).

My personal suggest is "go longer."

The APFT consists of Push-ups, Sit-ups, and Run. You know how many you must complete in each section (within a time-limit) to "maximize" the score.

Step 1: Condition yourself to be able to get past the QUANTITY (with correct form). Ignoring the time limit. Example (since I don't know the Army #s). USMC requires 100 Crunches in 2 minutes. Condition yourself to be able to do MORE than 100 (or whatever that number happens to be) Situps. Same applies to Pushups. For the Run, go LONG (like 3-4 miles).

You want to have MORE "fuel in the tank" at the end of the event.

Step 2. Start increasing speed bringing yourself closer to meeting the time limit of each event. Because you can now maximize the quantity (1), now it's about "beating the clock." You are trading Efficiency for Effectiveness. That's why you TRAINED BEYOND THE STANDARD.