I would say it does not lower the duty or the standards, and the fiduciary duty varies on the subject in question as well, so there's not an overarching fiduciary duty to first nations. However, certainly in this context, “best efforts” is intended to convey the fact that the government will take every step possible to achieve a result and to achieve an objective. To your question, this is a very high standard and signifies the government's commitment to ensuring safe drinking water.
Evidence of meeting #134 for Indigenous and Northern Affairs in the 44th Parliament, 1st session. (The original version is on Parliament’s site, as are the minutes.) The winning word was amendment.
A video is available from Parliament.