Beavers are fairly easy to trap... And shoot for that matter. HAHA
I was told beavers mainly swim around at night and you might need
night vision scopes ect....is that not your experience CJBS?
And beavers don't eat fish but otters do?
Beavers don't eat fish at all.
They do swim in a daytime too but maybe they enjoy dark hours more. Perhaps it's because then they aren't bothered by humans. But as I said before, it's possible to see them in afternoon or morning too. Simply don't make much mess and do not scare them away.
If you aren't sure about your possibility to shoot them in the night then think better about traps. They work well.
About shooting a beaver:
if you with to get rid of it then simply make a good shoot - it will die instantly or after some time because of injuries. If you wish to get beavers corpse too then try to blow his head off because otherwise it (even injured) will swim to one of it's holes and die there. You won't find it...