In the beginning was water. From this came Apsu (sweet water) and Tiamat (salt water - not to be confused with Tiamat, the five headed dragon from the old Dungeons and Dragons cartoon). They do what all brother and sister gods tend to do when left to their own devices (I'm talking about holding hands) and gave birth to Mummu (waves), Lakhmu (a big serpent), and Lakhamu (another big serpent).
The serpents held hands and gave birth to the heavens and earth. And these held hands to make all the great gods. All these baby gods made so much ruckus that Apsu and Tiamat decided that maybe it would be best to destroy them all and get a good night's sleep (come on, if you are a parent, you can say that the thought hasn't crossed your mind at least once...).
One of the great gods was Ea, the all knowing. So being all knowing and all, he found out about the plan. He captured Apsu and Mummu. This thoroughly pissed off Tiamat who then created an army of freaks to teach Ea and his siblings a lesson.
Ea, being all knowing and all, realizes that things don't look so good and tries to get some of the other gods to get off their lazy rear ends and fight. They are all scared. All except Marduk.
Marduk said he would beat Tiamat if he would become the supreme god. The agreed, held a big feast, had lots of fun and gave him a scepter and a throne.
Marduk went to battle armed with arrows, lightning, wind, a net, and a HURRICANE (thus the connection here). Tiamat came riding a storm being pulled by four huge horses. They fight.
When Marduk caught her in his net, Tiamat tries to swallow him whole, but as she opened her mouth, Marduk shoved the hurricane in it. There she sat, all bloated and full of gas, and Marduk shot her in the belly. I don't know if she popped like a balloon, but she died.
Moment of silence.
Marduk then caught her army of freaks and threw them into the underworld. Tiamat's body was then cut up and used to create part of the world in which we live. He created us from the blood of Kingu, her general. All the gods, awed by his strength and power (and perhaps feeling a little guilty) gave him their powers, making him top dog of Babylonian gods.