Well you know that hitting other players gets you damage, so i'll just give you the little tip that players are usually capping points, so go defend them instead of spawncamping their side like some do to get damage, which is the wrong way and a Dbag move. (But it depends on the match, anyways.)
Striker and Swords are the easiest way to get dmg since you can get to other places quickly to kill, and kill quickly aswell if done successfully, but I recommend also having a gun, just rushing in with only swords may get yourself killed if you're fighting a group.
Also remember that you need 2 Penta Trinkets and a set that gets you damage bonus, it's really useful for increasing those points, swords like Gran Faust/Divine Avenger also help a lot.
1. Buy some good seeds. I heard the Black Kat variety has great yields when planted with Heavy Swords and Three-Shot Guns.
2. Genetically modify those seeds so they will grow faster. Punch can help you with that.
3. Buy some good fertilizer. Some increase longevity for more fruiting seasons, some increase the growth rate of the fruit, others increases fruit size.
4. The game offers you a free Automated Tractor (AT), take advantage of it to increase your production rate.
5. Be sneaky and work hard. Loot other people's farms while protecting your own.
6. If possible, relocate to an area close to Lake Server*. Damage wont grow unless they have water from Lake Server. If you're close to the lake, you can make them grow much faster**.
*Lake Server is actually a group of lakes scattered across the U.S (and one in Europe).
**Lots of people use Lake Server so being close may not be enough. You need an uncrowded patch where you have a lot of open access.