A test animation of one tentacle, using dynamics. 

The arms have been welded on. A tedious task, since it involves vertices on all eight arms, but no more tedious than dealing with suckers. 

The first rigged arm was cloned in mograph. Using Current State to Object, seven duplicates were made. Each "shoulder" has ten vertices that match the ten vertices at the end of each arm, so welding the points together should go relatively smoothly. Suckers crossed.

I'm correcting and tweaking the mesh prior to rigging. Here I've placed the head and shoulders portion in a cloth surface to give the model thickness. From there I used the Fit Circle command to make eight individual circular edges so I can connect the tentacles to what is now the body. And for those who got this far in the post and are thinking about lunch or dinner choices, I recommend the Margherita pie at Joe's Pizza in Santa Monica and West Hollywood. It has a sweet flavor and is arguably the best pizza in Los Angeles. Just saying.