Is the no-killing approach in Undertale all about trial-and-error?

Solution 1:

There are often times hints inside either the dialogue of the monsters or the "Check" action that indicate the types of things that need to be done to pacify a monster. In addition I should note that in non-boss encounters you need not spare the monsters to still complete no-kill run simply running away is usually faster and can skip some of the puzzle solving aspect. Beyond that there is quite a bit of trial and error too figure out exactly how too pacify a monster.

There are no major side quests in Undertale (with two notable and obvious exceptions) but there are a number of monsters you can talk too and interact with that are tangential to the plot/game.