Giant Tarantula is one of the monsters seen in the elevator scene right next to the elevator containing Marty and Dana. It is not shown in the whiteboard.
It is first seen in its cube cell, crawling on the walls of it. It is later seen breaking into the Control Room during the Purge where Hadley then proceeds to shoot at it.
It bears the same look as a normal tarantula, except being aproximately three meters long.
In the DVD special features, there is a real live tarantula that is used in a cube, as apposed to the CGI one featured in the film. The reason for using the CGI one instead of using the real one in the elevator scene is unknown.