Here's a small guide for King of the Monsters 1. This applies to both the Neo Geo and Genesis versions.

One of your main attacks is your running attack. Run by holding C then forward, or double tapping the same direction. Make sure you keep your distance, unless you're using Beetle Mania whose run attack only has a few active frames. You'll use it in order to score knock downs. Press B to pick up an opponent that's lying on the ground, from there, you have a higher chance of winning a grapple (not so much in the Genesis version), but it still isn't guaranteed.

You produce power-up items by performing certain grapples (Up+A/B, Down+A/B, A+B, and the grapple that you do if you grab the victim from behind). It takes 10 power-up items to power up your character by a level. You can power up a total of 2 times. When you're powered up, you move slightly faster and your charge shot (performed by holding A+B and releasing when your character flashes white) does slightly more damage.

Once the opponent's lifebar is empty, keep knocking them down and going for the pins. It takes a minimum of 2 pins to defeat your target, and later opponents require more pins to defeat. Sometimes, you can get the computer in this nice loop where they would continuously run into your charge shot.

The outcome of the grapples is completely random, and is determined by the frame you grappled on. Once you're fully powered up, you'd want to avoid grapples at all costs, and stick to using charge shots from a distance upon knocking the opponent down, especially against later opponents as they have a higher probability of winning grapples than you. Normally, you can only survive the first 2 pins on Neo Geo and Genesis.