Vivement la fin des partiels que je puisse filer à la plage.

Hi Elaine, 

It is because of the expression 'vivement que'. It indicates a wish and this is the realm of the subjunctive.

Although the 'que' is separated by 'la fin des partiels' you could have said -

Take a look at the following answer regarding the expression 'vivement que'

https://progress.lawlessfrench.com/questions/view/vivement-que-plus-subjonctif

Bonne Continuation !