Is it really required?

Changes in INT, UAT and Production must be done following the standard Development and Release Management process, and we should avoid to make any changes on these orgs manually.
There are some scenario that can escape a bit from this process, like reproducing a bug, debugging apex code, or others that require to be done in a specific org or with a specific data set. However, before
thinking of asking admin rights in higher orgs, you need to make sure there is no other way.

You should only think about requesting higher access when:

1. You have attempted to perform the investigation in INT/UAT or the respective org using your current user rights
2. If 1. was not possibly, you have attempted to perform the investigation in a Developer org, where your user has "System Administrator" profile.
3. If 1 & 2 were not possible, but the investigation is quick to do (i.e <10 minutes), you can ask someone with current admin rights in these orgs to help you with their user

How to request Admin Permissions

In the org where you need permissions (i.e UAT org if you need admin permissions for UAT org), navigate to Salesforce Admin Request tab and create a request. After creating it, click on Submit for Approval.

Approval will be requested (via e-mail, including a URL to the record to approve) to the System Admin Rights Approvers queue, composed by Hugo Rosario, Dina Mendes and Julien Gasqueton, where only one of them needs to approve.

The approval history will display the status of the current request.

Upon approval, a Permission set group named System Admin Rights, will be automatically assigned to the requester (in 1-2 mins). This permission set group will grant most of the privileges of a system admin user (except Modify All Data). The permissions assignment last for 3 days and it will be automatically unassigned after the 3 days.