Kraid's entire body is resistant to damage, except for the inside of its mouth. You can get him to open his mouth by firing Missiles or Charge Beams at his central eye, which will cause him to roar. At the beginning of the battle, stand at the far right edge of the protruding platform, as the rest of the stone blocks will eventually be destroyed. Continue to jump and fire Missiles into his mouth, and use your beam weapon to shoot down the two spinning claws that Kraid repetitively throws at you. The spinning claws will allow you to restock on health or Missiles.
When Kraid receives enough damage, he'll destroy the remaining rock platform, and you'll then have to jump to the top of the three large spikes that he lodges into the wall. It's safe to stand on the spikes when they disintegrate, but just be careful not to get hit by them when he shoots the next set of spikes out of his belly. It's possible to jump on each consecutive spike, and dodge the next one by quickly rolling into Morph Ball.