There are following steps for Updated Mobile Number :
1. Login Employer ESI Portal
Link- https://esic.gov.in
Service-Employer-Employer Portal

2. Enter Login Employer Id and Password then new Page will be Open like below

3. Click on "Update Mobile Number of Insured Person" then new Page will be Open like below :

4. Enter Insurance Number (ESIC No) and search new Page will be Open and Update Mobile Number.
5. You can also Upload in Bulk and click on "Bulk upload of Mobile No."option" like below

6. New Page will be Open like below :

7. Firstly, You have to Download the Excel file from "Excel file Download" option. And make bulk file Update Mobile No. sheet. Then click on "Upload Excel file.