I’m terms of all the down-related trophies, one tactic I used was to camp downed players. Once you down a player, just wait near them while they stand up.
When they rise up, their health will be low. So you can proceed to down them again with the needed weapon.
Of course this is dependent on the player you are downing (some may fight back) but I was able to do this with when I came across a bot.