Self beaching drags itself up the beach and pushes itself off the beach 

https://www.facebook.com/video.php?v=997446350313796

This one wasn't a paddle boat either, but had claws as well:
http://laststandonzombieisland.com/tag/grillo/



Moritz

 

Back to the topic of paddleboats:

The concept of beaching by means of two "legs" at the front end somehow reminds me of the old practice of "Grasshoppering" some western river sternwheelers:
The could lift themselves and "crawl" successively over shallow sandbars by means of a system of capstan-operated hoists and two tall spars acting as "legs":

http://americanhistory.si.edu/onthewater/collection/TR_335811.html



So this one has paddles, and even has legs...