Accessing America's Critical Minerals Act of 2021 This bill establishes deadlines to complete the environmental review of critical mineral projects on federal land and sets forth related requirements to expedite the review of such projects under the National Environmental Policy Act of 1969 (NEPA). If an environmental assessment or environmental impact statement is required for such project, then all necessary federal review and permit considerations must be completed within 18 or 24 months, respectively. However, the review may exceed the time limit if the project sponsor agrees. The lead agency of the environmental review of such project must allow a state or local government, an Indian tribe, a project sponsor, or another appropriate entity to assume certain federal responsibilities regarding the environmental review of the project upon the request of such entity. Further, the bill authorizes a lead agency to determine that the requirements of NEPA have been satisfied if a state or federal agency acting under state or federal law has addressed specified factors, such as the environmental impact of the action to be conducted under the permit. If the lead agency does not make such a determination, then the agency must enter into an agreement with the project sponsor to set time limits for each part of the permitting process.