There are two ways to achieve this, please follow the below mentioned steps to approve multiple vacations. 

As an Approver:

-Click on the approvals icon on the top menu. 
-Select "Time Off Bookings" on the left pane. 
-Click the "Select All" option on the header in the "List Waiting Time Off Bookings" page or hold on to the "Ctrl" key on your computer keyboard and click on the names of users whose timeoff needs to be approved. (You can select multiple names by holding on to the "Ctrl" key.) 
-Click the approve button at the bottom of the page. (Find the attached screen shots for your reference.) 
As an Admin:

-Log in to Web TimeSheet as an administrator. 
-Click the Administration icon on the top. 
-Click "Historical Time Off" on the left pane. 
-Check the "Include sub-departments" option. 
-Click "Select All" on the header in the "List Historical Time Off Bookings" page or hold on to the "Ctrl" key on your computer keyboard and click on the names of users whose timeoff needs to be approved. (You can select multiple names by holding on to the "Ctrl" key.) 
-Click the "Approve" button at the button left corner.