There are some Mass members here who can probably give you more/better info than I can. I live in Maine but have family in Mass. I've looked into the rules a few times with the thought I might want to sneak out for a quick canoe hunt when visiting them, but have never actually done it.
Because Maine was once part of Mass, our coastal access law is pretty similar to theirs. Basically, you may legally fish, fowl, and navigate anywhere in the intertidal zone and anywhere on tidal waters.
However, that right is subject to several other sets of rules, including:
--State waterfowl and firearms rules. Mass firearms rules are a bit arcane, so study up to make sure you don't find yourself in trouble if you get pulled over for a bad tail light. They also have a much wider buffer zone around structures than many other states. In Maine that is 100 yards. I believe in Mass it's at least 500', and may be farther. It may also apply to public beaches, boat launches, and other public facilities.
--Town ordinances. Some towns may have ordinances with no firearms discharge zones. I don't know about Mass, but in Maine the intertidal zone is a bit of a gray zone for those rules. The town I grew up in had a no-discharge law, but did not enforce it on tidal waters--even well inland in a salt marsh. A town near where I live now is on a tidal river and does believe they can enforce the law in tidal areas. To be safe, check with the local police department about any town rules that may apply.
--Federal, state, and private refuge or conservation lands. The only one of these I have ever investigated in detail is the Parker River National Wildlife Refuge, which does allow hunting, but only in some areas, and the rules are complicated with various zones, some of which allow only walk-in hunting; others allow only access by boat. Town or private conservation land may also have rules that apply. Whether they apply in the intertidal zone is questionable, but probably better not to be sitting 10 feet into the mud on the Aububon Society bird sanctuary blasting away!
No idea what rules may apply on non-tidal freshwater sites, but you probably won't be chasing eiders there!
FWIW, my sister lives in Marblehead on the north shore, and in the fall and early winter and they frequently see folks hunting eiders on the islands around Marblehead and Nahant, so it can be done. I've also seen a lot of brant along the shoreline down there if brant are on your duck bucket list.