As a baby, the Alligator was kept as a pet by a Raccoon City resident before ending up in the sewers. When the t-Virus was released into the sewers, the creature became infected and adapted well to its effects, growing rapidly to over ten meters in length.
It made its first appearance in Resident Evil 2 where Claire encounters it while trying to reunite with Sherry in the Raccoon City sewers. Claire defeats it by tricking it into biting down on a gas canister that is promptly shot; the resulting explosion blowing its head apart. In the non-canon "Leon A" scenario, Leon encounters it when Ada is cornered by the gator, which then turns its attention to Leon. Other examples of infected alligators would be seen in Resident Evil Survivor.
It can also be found in Resident Evil Outbreak File 2 in the Zoo, the creature is named Gnaw. However it didn't grow to enormous size as its cousin from Resident Evil 2.
The Alligator reappears as a boss in Resident Evil: The Darkside Chronicles. In this scenario it is fought by both Leon S. Kennedy and Claire Redfield. This version of the fight shows Leon and Claire at first attempting to kill it by igniting a leaking pipe valve. However this only badly burns it, forcing the duo to trick it into biting down on a gas canister that is promptly shot; the resulting explosion blowing its head apart similar to its fate in RE 2.
Resident Evil 2 The Alligator can be defeated in Scenario A by simply shooting it (though the monster is really tough), causing it to eventually smash a hole in the wall and escape. A small amount of ammo will appear a little later on. If the Alligator is defeated this way in Scenario A, it will come back again in Scenario B. In this Scenario, shooting the monster until it collapses will finally kill the creature for good.
The other more economical method involves releasing an emergency gas canister which the Alligator promptly picks up in its mouth. When the canister is shot, it explodes, taking much of the Alligator's head with it. Defeating it this way means it can be killed with only one hand gun round. Also if the monster is killed this way in Scenario A, it will no longer come back in Scenario B.
Resident Evil Outbreak File #2 In Outbreak File #2, the only strategy is to just swim over the area where it lives. If you really need to shoot it, stay on the dry land but close to the water. Gnaw eventually will swim to the edge and try to attack you on land. When it trys, just shoot it. It will take quite a few shells from the shotgun to take it down, but using the Hunting Rifle will kill it in two shots.