I'm sure this has been asked before, but which warlords are you able to recruit within the main storyline? I may be interpreting the "4 turns" thing wrong as well. I'm assuming it as 4 of MY turns or else a 2 turn KO on a warlord seems hard. Managed to beat the Greenleaf warlord on my turn 7 (my 4th turn) with the eevee, but I didn't get him.
to recruit the unique warlords (Muneshige, Yoshihiro, etc.) you need to either beat them within 4 of your turns, beat them with a critical hit or beat them before you take any damage, and also you will need to beat them with a unique warlord, (the Hero, Oichi, Muneshige, etc..), but some of the unique warlords aren't available to recruit until you finish the game
Considering it didn't work for me when i tried it in Grassleaf, i'm assuming the water area also doesn't allow you to recruit the warlord, and only until you reach the northern regions are you able to.