I am clear that a grounded figure entering hindering terrain from clear has to stop. I am also clear that when they leave they move at half speed. However, in regards to grounded figs moving through hindering terrain FROM adjacent hindering terrain, do they move at half speed or do they have to stop ever single square?

Example:
A=my fig IN hindering terrain
E=the enemy I want to base
H=hindering terrain
x=clear terrain

You'll move at half your Speed value. As long as you do not enter the Hindering from a Clear terrain square... you can move.

So, assuming your figure had a Speed value of at least 8... he would be able to travel through all the Hindering terrain squares and end up base-to-base with the opposing figure.

isnt there a new rule that u have to stop if u enter a hindering terrain?

There is no new rule that I'm aware of. You always must stop when entering hindering terrain from clear terrain (Leap/Climb, Phasing, Flyers excepted).

Moving from hindering halves your movement immediately.
If you move from hindering to hindering you don't have to stop. If you move from hindering to clear and back to hindering again then you have to stop.

What about characters with hypersonic speed?

what if you have a fig with a 5 for his movement how would u cut that in half?

round up

Hypersonic speed doesn't ignore hindering terrain, so they have to abide by the same rules as normal characters as far as stopping when entering hindering and halved movement when starting in hindering.