The game's combat system takes getting used to. Even if you think you know what attack a Kaiju will come at you with, that doesn't guarantee it won't hit you. Get to know both your parry and dodge attacks. Parrying is more effective, as it leaves the Kaiju open to attack sooner. However, it's also risky, as it doesn't work as simply as evading. Practice both moves and see what's best for you.
You'll start the game with a default Jaeger (robot) unit, the Coyote Tango. When you get the chance, unlock additional models in the game. Gypsy Danger, for example, is the most effective robot when it comes to delivering hits and evading incoming attacks. It may take a little while to unlock, but it's worth it. Check out the other units, too.
Customize, customize, customize. Whether you're shopping around the official Jaeger shop or making a stop in the shady Black Market, you'll find various pieces of armor and weaponry that'll make your Jaeger a better fighter. For instance, we upgraded our hand blades with the chainsaw ones. Not only does our robot look cooler, but it also delivers stronger hits to the Kaiju. Test different types and see what they do for you.
Read up on the Kaiju once you unlock their files. You may think it's unnecessary reading, but you might actually learn a thing or two the next time you face them. Plus, you may spot them in the movie. Never hurts to have some additional trivia to wow your friends.
Save your weapon and special attacks for when they really count. As you proceed through a fight, you'll charge up one of these two, depending what's available to use against the Kaiju. Once it activates, though, don't waste it. Try to save it for one of two occasions. The first is an end-of-the-match moment, where you could earn an extra coin bonus just for finishing off your Kaiju adversary in style. The second saves your skin, in case you're running low on energy and need to get back in the fight.