Can Barrier be placed on grounded and go to elevated.

Example:
On Hulk Map
Character A occupies middle of elevated terrain
Character B is 8 square away from elevated terrain with a 7 range
can character B place barrier on grounded and then place barrier on elevated to surround character A so he can not move off of elevated

No. All the blocking terrain markers placed by using Barrier have to be adjacent. Since there is an elevation change there, they would no longer be adjacent.

Barrier pieces (yes there is a way to "rules lawyer" this, or to be a "dink") have to all be adjacent to each other. Objects/barrier tokens on elevation X are not adjacent to objects/barrier tokens on elevation Y.

Ask yourself, "can a figure, without any special power or Leap Climb, make a close combat attack against another figure if they are 'next to each other' on different elevation?"

No, they can't.

Also, elevation changes are only adjacent for close combat purposes. So they will not be adjacent on stairs/ladders.