Yes, “best efforts” is a very high standard.
You're right. A a lot of “best efforts” references are in contract law, but it's not exclusive to contract law. Basically, in this situation, the minister would have to take every possible step she could to ensure safe drinking water on first nation lands. She would have to work with her colleagues in cabinet. She would work with officials to ensure safe drinking water was delivered.
In terms of standards, in law there are “reasonable efforts”. That was used in the settlement agreement. It's a lower standard. Still, you have to take significant steps to achieve a goal.
In “best efforts”, you have to make your maximum effort to achieve a goal. If you do not achieve that goal, you would not necessarily be penalized for that, but if you did not make every attempt to achieve the goal in this, the context of this legislation, then the minister would be failing in her obligation. It is slightly lower than “must ensure”, but it is a very high standard for the minister to have to achieve.