Alright, i'm seeing a few things there.

I'm seeing a class that could be the tentacular rogue or shadow dancer, but it ends up being another melee-fighter.

If you want to call it "shadow", maybe you should get in a few shadow powers

Now let me squeeze out this brainfart...

First, the class lacks options, a lot, in fact, this would be much more balanced as a 10 lvl prestige class than a 20 level base class, and even then it maybe light on options.

Second, you have missed replacing a "spell" reference in the text of Quick Tentacle, it misses damage type (bludgeoning ?), and honestly, please find a better phrase for the spider climb effect...

Third, Fast Movement needs progression. Most "fast" classes allow up to +30ft over 10 levels

Fourth, Tentacular Insight seems to give +10 AC and ref saves , which is good now for the skill, you end up with :

+10 Knowledge: Planes, AC, and Reflex saves.
+8 Escape artist
+6 Hide
+4 Move Silently
+2 Survival

Sorry but survival +2 seems to say "i didn't know what to put there"

Now if this class needs stealth to do its job (it's a shadow after all), you should give better bonuses to hide and move silently, they are much more needed than knowledge.

Also, putting the AC and reflex bonus in a seperate ability would allow you to put in more fluff (just an ability name is often enough to flesh out the fluff) even if you keep the same progression.

Fifth Tentacular Slam, no big deal but you are mixing sneak attack and precision damage, precision damage is a type of damage that doesn't work on undeads,oozes and such
sneak attack is a rogue feature that deals precision damage and needs flanking or flat-footedness to trigger

Sixth, the Great tentacle. This looks like a "fixed" shadow step. The shadow dancer would need something like this. Your class would probably gain more benefits from manifesting more tentacles progressively, get multi attack, and finally have tentagon remove all related penalties.

What misses there is the ability to manifest tentacles through the shadows, like all those horror movies where you know the guy passing the shadow is going to get grabbed

Think about it, you're watching the guard, and commanding your tentacles to grab him 30ft away from where you hide, that would be a nice touch.

Tentagon seems big to me, over capstone. You get to deal 8 full attacks in a round (totalling 24 straight attacks, 6d8+1d6+20 each...), at will. With a decent strength, that's mighty big, should you hit you could total 144d8+24d6+480+24*str mod, average over 1000 dmg in a round. Did i say you can do it at will ? Did i say it was OP ?

All in all i'd say this would be a terrific 10 level prestige class, but IMHO you should rework it.

As i re-read my post, i'm finding it a bit harsh, i liked the theme, the fluff , and i'm just a big fan of tentacle thinguies

I'm just trying to point out possible/probable flaws, don't take it too badly, this is good work. You have the potential to make it great.