There is no need to do any coding to use the Beta version. Just copy it on top of your existing plugin and it will automatically work, you don’t even need to deactivate the old one.
I can see the following in your HTML:
[code:2086j2j0]<ul id="suckerfishnav"></ul>[/code:2086j2j0]
It presumably looks something like the following in your header.php file:
[code:2086j2j0]<ul id="suckerfishnav"><?php suckerfish3(); ?></ul>[/code:2086j2j0]
Remove that and the old menu should be gone.