Why are the assassins so obsessed with Kai in the first place? Yes I know he foiled their first assassination attempt, but that was a complete coincidence. If they're that worried that he will save the princess a second time how about they just attack her when he's not there? He's not her bodyguard or anything, they're acquaintances at best. And they clearly have the connections to completely infiltrate the school without even being suspected so don't pretend they wouldn't be able to keep tabs on him.
You have the fake teacher dude who apparently has skills to move around instantly and strike before anyone can react. And he's really an assassin. So why doesn't he assassinate...the target with those skills? He seems willing to use them on just about anyone else. But not the person he actually wants to assassinate, even when nobody suspects a think and they completely have their guard down...
But wait you say, they wanted to make it look like an accident. The first time, yes...but then they come up with the most over-the-top completely blatant assassination plan in the known universe. Which is pretty weird in of itself, you know, and they never explain it. I mean, I can almost buy that they initially wanted it to look like an accident and then when that didn't work they decided that it wasn't that important (though none of this is actually shown to the audience). However they went straight from "make it look like an accident" to "let's create this elaborate plan involving a giant barrier, trapping dozens of unrelated people, and killing the target with a giant zombie dragon with witnesses all over the place". There's stuff in between you know...