Most of the skills require a roughly equivalent target for the combat skills to gain - on any pet. On the other hand, it takes a tough target to gain more than 0.1-0.2 towards training.
First thing to do is make sure your beetle is 1-slot. If you didn't fix an old 3-slot one be releasing and retaming it, it's too late.
It's usually best to train the first level first, and this pretty much requires the following.
- Make sure it is bonded. It will die a lot if the things being fought switch targets.
- Get an existing 3-4 slot pet, preferably one that has been trained for high resists already, or with naturally high resists. Alternatively, get someone else to bring their 3-5 slot pet, so you have someone to talk to.
- Have the higher-slot pet tank versus a named mob (such as Swoop), or against something tough in Shame (crazed mage, eternal gazer, etc.) with the beetle assisting.
Now, for skill training, look for stuff that is at your pet's wrestling and tactics level +/- 20. For a beetle starting out, I typically use the orc fort west of Umbra at the mountain entrance (or similar forts north of Luna, or in the snowy mountain areas). If you've not raised it to 2/5 (And raised HP and resists) yet, you'll have to do a lot of vetting to keep it alive - and you'd have to kill 10,000 orcs (sounds like a Drizz't novel) to even come close to getting a training level. Once you have it at 2/5 or 3/5, though, you might be able to just park him inside the fort (maybe even the one in Yew) and let him go to town. You'll get some resisting spells gains from the orcs, parry gains that won't actually show until Wrestling hits 100, and lots of wrestling, tactics, and anatomy gains. Also, poisoning gains if you put it on already. Once you get between 80-90 Wrestling, you'll want to go looking for something with 100+ wrestling for skill training.