One major thing to work on for grapple is balance, this is applicable to all the other styles as well, in my beginner tutorial, linked at start, I briefly explain footnotes in balance under ground control, and in my aikido adept tutorial, also linked at start, I go into more detail on balance in the more about balance section. However I would like to provide some more context to balance and maybe try to give a little more help. Really the key to understanding and achieving balance is through understanding center of mass as I explained in those tutorials. Once you can understand how to know where the center of mass is you will control your balance a lot better. If you know where the center of mass is if you stretch your body as far from it as possible you will lower your moment of inertia, essentially you slow down, and vice versa. It is easiest to balance when you have more than 1 contact point on the floor, for this reason it can be beneficial when doing no-grab to drop down, then kick while putting one of your hands on the floor, rather than the usual when grabbing to just go for a kick or knee. If you would like more explanation than here simple message me.

In all mod styles, besides probably boxing and kicking (ironically), you need to be able to catch kicks, here is what Renixxx has to say about it:
"The most important thing for catching kicks is timing. You need to watch your opponent's moves and analyze them. When you see a kick coming, position your arms in way so that the kick lands between them. A great tip is to relax your elbows and wrists - when the kick lands the force might slightly contract them and trap your opponent's leg. When that happens contract your arms and position yourself into a well grounded stance. Be careful with experienced players because in most mods leg joints are strong enough to lift you up - that's why you need to be grounded. To prevent being lifted move your lower body closer to your opponent and pull your upped body backwards. In that position you gain access to multiple takedowns and sweeps - it's up to you to choose the best move in your situation."

Something also applicable to all mods is learning to control momentum, but I'm putting it here because I feel in this mod you benefit from good momentum control the most. Being able to control momentum pretty much requires some understanding of center of mass, be that innate or acquired understanding does not matter. To control momentum you need to raise and lower your moment of inertia, doing this is simple. You pull in your body, making your mass all closer, to have a lower momentum of inertia, and vice versa to raise it. What is the benefit of doing this? Angular acceleration is why, if you begin a spin with a high moment of inertia, i.e. body outstretched, then bring the body in close, you will spin much faster than if you tried to start the spin with arms and legs close to center of mass. Now it doesn't really make sense to do a flip like this however for other reasons as it doesn't actually work out so perfectly, but the idea is there. If you initiate a spin and can bring in your joints towards your chest or wherever the CoM (Center of Mass) is, you will spin faster. Whereas also it can be beneficial to slow down a spin so that you will not arrive at an opponent having spun too far, so if you behind to spin too far, be that towards the opponent, or out of the ring, try to raise your moment of inertia.

Toribash is a physics game and the two most important things to being a good player is understanding your position and your momentum. The way to get the strongest kicks and punches is to gain speed and transfer it into rotational momentum and hit your opponent with that energy. The key is to gain speed by contracting and extending joints, great power is in the knees but make sure to use your entire body such as hips glutes chest lumbar pecs shoulders to complete the motion. Tip: don’t underestimate relaxing joints! Extended or contracted joints move with a fixed force so relaxed joints actually have a higher top speed, this is only in rare situations though, I have found them to occur most with hips when contracting the knee and pecs when putting your full body into a single haymaker. Extended, held and contracted joints are also very stiff so make sure to learn which joints to relax to increase your fluidity. A good exercise for this is to practice by relaxing all every turn, this will show you through your ghost how you are moving and what you can do to use that. The command /sm 1 can also tell you how fast you are going

Lenshu is definitely a mod where you want a reliable opener, here is what Goldcloud has to say: "
The opener can be found described step by step on Goldcloud9's post

In kicking mods it is essential that you can block and dodge, so prediction is a vital thing to learn, understanding what the enemy is planning and can/will do. No one can really tell you how to begin to understand prediction, it simply comes with experience, but here are some things to look out for. Pay attention to how smart they play and how they play, are they aggressive forcing combat, are they passive avoiding combat, do they let you make moves and react to them. Knowing these things will let you know what they will do in what position, of course people know this and will randomize what they do to throw you off. That is why the ability to predict simply comes with experience and enough of a spritz of luck thrown in. For example, if you are playing a kicking mod, lets say boxshu, and they get into a launch position. If they are aggressive, they will go right for the launch and go as fast as possible. If they are passive they will wait to see if you move then if you don't will possibly come towards you especially if they are low on points. If they sorta just let you do your thing they will wait till they see you leave an opening or get to close. One thing to note is the most experienced players will oft go for the last option as it is the safest and most controllable. The smartest players try their best get themselves into repeatable positions, but around here we try to spice the game with as much style as possible. Being unpredictable can be a way to beat stronger opponents too, so always keep this in mind