Just putting this here for posterity, because I don't think the exact way is spelled out anywhere on this page. The way the Full Game run gets past the unbeatable second stage of Tech Island is editing the game's registry to unlock the next world.

To do this, open regedit and navigate to Computer\HKEY_CURRENT_USER\SOFTWARE\AT Interactive Studios\Baby Coyote. Edit the levelReached value and change it to 12 (hexadecimal). This can be done while the game is running, as long as you're not on the stage select screen while doing it.

Also, a while ago I made a patch that slightly moves the death plane that covers the teleporter exit. This makes it possible to beat the stage and the subsequent boss, rather than skipping to the next world by editing the registry. It's a simple BPS/IPS patch for the file BabyCoyote/Baby Coyote_Data/data.unity3d that can be applied with any common rom patcher.