Fact: If a neighbor's tree's roots encroach upon your property, even though the tree itself is only on the neighbors property, you have the right to cut the roots to your property line. If that kills the tree, it is not your fault. The same is true for encroaching tree branches that hang over your property.
It certainly would be prudent to fire off another letter, demanding that the neighbor remove the shed. The letter should be sent first class mail and certified (they can refuse to sign and/or pick up a certified letter in which case it will be returned to you). It makes sense to refrain from starting a Hatfield v. McCoy type feud by just destroying the shed prior to affording the neighbor a reasonable period of time to remove it. Alternatively, if the area where the shed is placed does not bother you or otherwise adversely affect your use and enjoyment of the property, write the neighbor and tell them that they may continue to use the land, subject to your right to terminate this permission at any time. In doing this, you remove one of the essential elements of adverse possession: the element that the use be (notorious) without the true land owners permission.
Bottom line: Liability, alienability (ease of selling land), and prudence dictate that you take the steps necessary to remedy this matter, to YOUR satisfaction, sooner rather than later.
Being an a$$hole, I have an opinion. Play nice at first and if they don't cooperate, send Vinny over to deliver a "message."