Fearless: I had no idea what "no village slayers" meant. So I killed him with shadows of players. That didn't work. Then I used story npcs. That didn't work either. Irritated, I just went solo and did the mission in chapter 14 with him and edax, testing out if I only had to kill him and seeing if finishing the mission was not required. It wasn't. As to what I used against him, I used a speed build with a wind chain and sickle. Relatively easy fight.
Long Live the King: I wish I didn't get this trophy first. I chose the mission with a single king in phase 16, and used a water chain and sickle. I had Hasegawa Heizo with me, who has conviction, which makes your recoveries a lot more useful. I'm not sure what the minimum hp limit for conviction is to trigger, but my guess is just two recoveries worth after you have 1 hp remaining. So after 35 minutes, and other time consuming failures before that, I finally took him down. Then I went to get the other trophies, and facepalmed after Fearless. The king in the last mission of phase 17, The Ultimate Challenge, happens to be one of four bosses in that mission, thus meaning his health is decreased drastically. He also conveniently happens to be the first boss.