Instructions
Save the game before facing Laura -- if after a few tries you find that you're not powerful enough to defeat her, you can reload your save and track down some more powerful dinosaurs before returning to her.
Use fire-based dinosaurs in the fight against Laura, since both the dinosaurs she will send against you are wind-based and thus vulnerable to fire. Laura's first dinosaur, the Ceratosaurus, is relatively easy to defeat; her second, the Alpha Dilophosaurus, is more of a challenge, but a sufficiently high-level fire dinosaur should make short work of both.
Use the Fire Power move, if you have it available, against both of Laura's dinosaurs for maximum effectiveness. The Fire Power move is granted to the Megaraptor when it achieves level 10 -- dig up a Megaraptor and use it in random battles until it obtains the necessary power. You can obtain a Megaraptor at the beginning of the game by exploiting a peculiar cheat: enter the D Site Branch building in Euro Town, select "Connection Room," click "Connect to Nintendo WiFi Connection" and then press the "B" button to exit once you've connected. Repeat this process 50 times and you'll receive a free Megaraptor.