How to create tentacles moving with the wind?

You can achieve this by using a Soft Body Lattice to automatically deform your mesh and react to the physics. The advantage of this over making the whole mesh a Soft Body is that each tendril can be given its own soft body settings (so some could be stiffer or heavier than others) and also your actual mesh geometry will not affect the simulation (making it simpler and quicker to simulate without having to change the geometry of your mesh).

To start, create a Lattice object and increase 'U' to give it enough detail in that direction. Scale it and position it over your 'tendril'. After re-scaling, ensure you 'Apply Scale' to ensure the simulation is consistent.

If you need to you can reposition each vertex of the lattice in Edit mode so that it evenly surrounds your mesh (in my case I used a straight extrusion for simplicity).

Anchor the 'base' of the lattice by adding a new Vertex Group (we'll call it 'Anchor') and assigning the 'base' vertices to that group.

Similarly, on your mesh, create a new Vertex Group (in my case named 'Tendril') and in Edit mode assign all vertices in the tendril to that group.

Select the lattice, hold Shift and select the mesh, press Ctrl+P and parent the lattice to the mesh so that it follows it.

Select the lattice and add Soft Body physics. In the Goal, set the Anchor as the Vertex Group, increase Stiffness to 0.999 and Default Strength to 1.0. Set the rest of the soft body settings as desired. For me I set the Object Mass as 0.1kg, set the Edge Springs to 0.8 Pull and Push and Bending to 2 and enabled Stiffness.

Select the mesh, add a Lattice deform modifier and set the Target to the lattice, with the Vertex Group set to Tendril.

Now run the simulation and you should have the tendril reacting to the soft body physics.

The mesh should now respond to forces and movement. For multiple tendrils, simply repeat the process - adding more soft body lattices and further groups and modifiers for each tendril.

Blend file included

It might be doable with only Cloth Physics but I don't know it enough to find the settings that would prevent face collisions, so here is a method that works:

• Create a vertical plane with for example 5 different faces, assign it a series of vertex groups, the 2 bottom vertices will be group1, then the group above will be group2 and so on. Also create a new group that will be the Pinning group: in Weight Paint mode paint a gradient that goes from red on the top to blue on the bottom. Give this plane a Cloth physics and in the Shape > Pin Group select the ^pinning group you've created.

• Create 5 bones that follow the vertical plane, with the head at the position of each plane's group. Deparent each bone. Give each bone a Bone Constraint > Child Of, for the bottom one choose group1 as Vertex Group, and so on. Each time press on the constraint Set Inverse button so that the bones stay in place.

• Parent the tentacle mesh to the bones With Automatic Weight.

• Create a Force Field > Wind to test the rigging.