Following is a publication that lists chemical applications that can be done for the nymph stage, April through June, (2 generations per year) and a systemic applied as  a drench to kill the females feeding and laying eggs over the winter through early spring.
https://extension.psu.edu/hemlock-woolly-adelgid

Given the size of the tree, these applications should be done by a certified pesticide applicator. If you hire someone who is also a certified arborist, they can tell you if the tree is worth saving.  Sometimes, if 50% of the tree is already dead, you only have another season or two, no matter what you do. early treatment is essential in this case.  if you have other hemlocks on your property, you should be checking the tip branches for signs of the waxy white coating and they should be treated as well. These pests don't fly but are transported by wind, rain and animals (mostly birds).

You can find a certified arborist with a pesticide license here (put in your zip code, click on a name and you can see their credentials):
Find an Arborist