Learn Croatian: Hipnoza će šokirati svu publiku. - Hypnosis will shock the whole audience.

It is acting as a perfective verb here. Šokirati is a dual-aspect verb, which is common for loanwords ending in -irati. This means the exact same word can describe an ongoing process (imperfective) or a completed event (perfective). Because the sentence describes a single, sudden event that will be completed, context tells us it is perfective.

Why is svu used here for "the whole", and what is its base form?

The dictionary form is sav, which means "all" or "the whole". It changes to svu here because it is modifying publiku, which is a feminine singular noun in the accusative case (since the audience is the direct object receiving the action).

Could I use cijelu instead of svu to mean "the whole" audience?

Yes, you can say cijelu publiku and it means practically the same thing. While sav usually leans toward "all" (the collection of people) and cijel leans toward "the entire" (one unbroken unit), they are often used interchangeably with collective nouns like publika.

Since this is the future tense, why doesn't the infinitive drop its final "i" to become šokirat?