The following table displays the permissions required by administrators for approval objects:

ObjectallowCreateallowDeleteallowEditallowReadmodifyAllRecordsviewAllRecords
AdhocApprovalGroup__cTRUETRUETRUETRUEFALSEFALSE
AdhocApprovalProcess__cTRUETRUETRUETRUEFALSEFALSE
AdhocApprover__cTRUETRUETRUETRUEFALSEFALSE
ApprovalJob__cTRUETRUETRUETRUEFALSEFALSE
ApprovalProcessInstance__cTRUETRUETRUETRUEFALSEFALSE
ApprovalRuleAssignee__cTRUETRUETRUETRUEFALSEFALSE
ApprovalRuleDimension__cTRUETRUETRUETRUEFALSEFALSE
ApprovalRuleEntry__cTRUETRUETRUETRUEFALSEFALSE
ApprovalRule__cTRUETRUETRUETRUEFALSEFALSE
Approval_Matrix__cTRUETRUETRUETRUEFALSEFALSE
Approval_Process__cTRUETRUETRUETRUEFALSEFALSE
Approval_Request_History__cTRUETRUETRUETRUEFALSEFALSE
Approval_Request__cTRUETRUETRUETRUEFALSEFALSE
Apttus__APTS_Admin__cTRUETRUETRUETRUEFALSEFALSE
Apttus__APTS_Agreement__cTRUETRUETRUETRUEFALSEFALSE
Apttus__Term_Exception__cTRUETRUETRUETRUEFALSEFALSE
AsyncActionInfo__cTRUETRUETRUETRUEFALSEFALSE
Backup_Approver__cTRUETRUETRUETRUEFALSEFALSE
FormulaField__cTRUETRUETRUETRUEFALSEFALSE
Global_Discount_Policy__cTRUETRUETRUETRUEFALSEFALSE
OpportunityTRUETRUETRUETRUEFALSEFALSE
ReminderInstance__cTRUETRUETRUETRUEFALSEFALSE
Reminder__cTRUETRUETRUETRUEFALSEFALSE
SearchFilter__cTRUETRUETRUETRUEFALSEFALSE
Term_Exception_Approval_Condition__cTRUETRUETRUETRUEFALSEFALSE
Term_Exception_Approval__cTRUETRUETRUETRUEFALSEFALSE

For information on setting object permissions, refer to this Salesforce article.