Calmed Beetles with Spores
It sounds like you’re at the right event, but I have found participating in it to be a struggle sometimes.
First off, to calm them, they need to wander near the mushrooms. This step can take a while, especially if other people are doing the event. The spores have a limited range so make sure the beetle is up close before hitting the mushroom. You can also grab a “fishing rod” of sorts from the nearby hylek rooms which have some useful skills.
If there are too many people around completing the event, just ask if you can calm one. I prefer to stand at the mushroom which is just outside their pen, but so do a lot of other people
On what may be a red herring, I recall the achievements being mixed up for the Nuhoch at one point. Try participating in all the Nuhoch events, especially trying to complete the first one.
The fishing rod thing’s 1 skill will pull them to you so just stand next to a spore and use it on a beetle. There is no need to wait.