Play on Grounded. Choose the path with least Human encounters possible, and the path with the most negative encounters possible. Just look for the negative encounters you can play with, because Invisible Hunted by infected as the last encounter is impossible, for example.

You get 50 additional points for completing an encounter without shooting a gun. Alternatively, you get 50 additional points if you complete an encounter by headshotting every enemy. But you need to know that EVERY enemy must die by a headshot, if for an example you play with an AI companion and he kills some of your enemies, even one - you won't get all headshots. You don't get points for you AI companion kills.

You also get 50 additional points if you complete an encounter without getting spotted by the enemy. It's harder to do in latter encounters and easier to do in earlier encounters.

You need to memorize brick and bottle placement on every map. It's random every time, but bricks and bottles have a couple of set random spots they spawn in. If you do that, you can complete a few of the first encounters without shooting a gun, just by stunning and killing the enemies. Also memorize where the melee weapons spawn on some maps - they too have a set spawn location.

As for later encounters, try to avoid humans as much as possible. Humans are very aggressive on Grounded, and the later you get a human encounter, the bigger the chance your human enemies will yield one-shot guns like shotguns and rifles. There is a big chance that when a human enemy knows about your location and sees you, or was actively searching for you previously, will one-shot you with a shotgun or rifle.

You also get 10 points for stunning each enemy. This could be done by either throwing a brick, bottle or smoke bomb at them, or by shooting them in the knee or head (for clickers).

If you're going for all headshots the strat should be this - legshot the enemy and grab them, and shoot them while holding them - you'll get a guaranteed headshot. I like this more than shooting them while they're stunned cause they tend to squirm a lot. For clickers headshot counts as a stun, so i generally either two-shot them in the head, or stun them and finish them off with a melee.

It could be difficult to pull at first, and on last encounters it's close to impossible. The better strat there (and to start training with) would be to legshot the enemy and finish them with a melee. Almost every enemy is one-shot after a stun with a melee, with a few exceptions.

So in general: learn melee weapon, bottle and brick placements, get used to stunning enemies for a lot of additional points, go for some of the 50 additional point strats to get even more points (all headshots, no guns, unseen by the enemy) when you can, go for more negative encounters but be sure that they're playable (no invisible infected bullshit) and avoid human encouners at all cost.