What role and access level should I have to accomplish HubSpot migration?

For migration from or to HubSpot CRM, you need to have App Marketplace Access permissions for your user: 

For the efficient migration, your user also needs to have access to create and edit all objects records that you are planning to migrate. Otherwise, you won't be able to see and enable those objects in the wizard. Below you can see the list of permissions that are required for the successful data migration: 

• 'crm.objects.companies.read', // read Companies. 
• 'crm.objects.companies.write', // create/update/delete Companies 'crm.objects.contacts.read', // read Contacts/Engagements
• 'crm.objects.contacts.write', // create/update/delete Contacts/Engagements 'crm.objects.deals.read', // read Deals '
• crm.objects.deals.write', // create/update/delete Deals
• 'crm.objects.owners.read', // read connection owner; read Users 'crm.schemas.companies.read', // read Company Properties 'crm.schemas.companies.write', // create/update/delete Company Properties 'crm.schemas.contacts.read', // read Contacts Properties
• 'crm.schemas.contacts.write', // create/update/delete Contacts Properties 'crm.schemas.deals.read', // read Deals Properties
• 'crm.schemas.deals.write', // create/update/delete Deals Properties
• 'oauth', 'sales-email-read', // read Emails (Engagements)