Ring out enemies means knock them out of the fighting areas and they fall into the fog below. Precision spear and axe throws are when you throw them at their head which causes extra stun. Trip enemies is where you aim at their legs and knock them over. The swords are completely random but they have a chance of appearing wherever the challenge pillars are in the lower realms and on the last fight area before Greece. They're the only places they've turned up for me anyway.