Learn Hardcore Dutch: Tijdens het tentamen moet Sofie zich goed concentreren, anders raakt ze snel afgeleid en verliest ze haar concentratie. - During the exam Sofie has to concentrate well, otherwise she quickly gets distracted and loses her concentration.

Both are correct.
Putting Tijdens het tentamen at the beginning emphasizes the time frame (during the exam) and then, because of the verb-second rule in main clauses, the finite verb moet must come immediately after it:

Tijdens het tentamen → moet → Sofie → …

So the order is: time expression – conjugated verb – subject – rest.

Why is it het tentamen and not de tentamen?

Tentamen is a het-word (neuter noun) in Dutch, so it takes the definite article het:

het tentamen – the exam / test
plural: de tentamens

You simply have to memorize the gender of nouns, but a lot of academic/Latin-based words like examen, tentamen, probleem, systeem are het-words in Dutch.

Why is moet in the present tense when we’re talking about something that happens during the exam (a specific time)?

Dutch often uses the present tense to talk about:

general rules or necessities
things that will happen in the (near) future
habits or typical behavior

In Tijdens het tentamen moet Sofie zich goed concentreren, this is more like a rule or requirement: Sofie has to concentrate (whenever she is taking an exam).

You could make it explicitly future with zal moeten, but that’s not necessary here:

Tijdens het tentamen zal Sofie zich goed moeten concentreren. (more specific future situation)
Tijdens het tentamen moet Sofie zich goed concentreren. (sounds like a general rule, but can also refer to a specific exam)

Why do we say zich concentreren? What is the role of zich?

Concentreren is a reflexive verb in Dutch: you almost always use it with a reflexive pronoun zich (or the form that matches the subject):

Ik concentreer me
Jij concentreert je
Hij / zij / Sofie concentreert zich
Wij concentreren ons
Jullie concentreren je
Zij concentreren zich

So with Sofie (3rd person singular), the correct form is zich:

Sofie moet zich goed concentreren.

Leaving zich out (Sofie moet goed concentreren) is ungrammatical in standard Dutch.

Why is it zich goed concentreren and not zich goed geconcentreerd or zich goed geconcentreerd zijn?

Zich concentreren = to concentrate (the action, the process)
Geconcentreerd zijn = to be concentrated / focused (the state)

In this sentence we talk about what Sofie has to do, not just how she is:

moet zich goed concentreren → must concentrate well (perform the action)
moet goed geconcentreerd zijn → must be well-focused (describe her state)

Both are grammatically correct but slightly different in nuance. The original sentence focuses on making an effort to concentrate, so zich goed concentreren is the natural choice.

Why is it goed concentreren and not goede concentreren?

Goed here is an adverb, modifying the verb concentreren (how she must concentrate). Adverbs in Dutch do not get an -e ending:

goed slapen – sleep well
hard werken – work hard
zich goed concentreren – concentrate well

Goede would be an adjective, which you use before a noun:

goede concentratie – good concentration (noun!)

So:

zich goed concentreren (correct)
zich goede concentreren (incorrect)

What is the function of anders here, and why does the word order change after it?

In this sentence, anders means “otherwise / or else” and introduces a new main clause:

…, anders raakt ze snel afgeleid en verliest ze haar concentratie.
…, otherwise she quickly becomes distracted and loses her concentration.

Because anders is in first position in that new main clause, the finite verb raakt must come in second position (verb-second rule again):

Anders raakt ze snel afgeleid.
(1. anders, 2. raakt, 3. ze …)

This is the same pattern you see with other sentence-initial elements in Dutch, such as time expressions:

Morgen ga ik naar school.
Dan zie ik je weer.

What exactly is happening in raakt ze snel afgeleid? Is afgeleid a separate verb?

The core verb here is raken, which can mean “to become / to end up” in this kind of construction.
Afgeleid is the past participle of the separable verb afleiden (to distract), but here it functions as an adjective: afgeleid = distracted.

So literally:

raakt ze snel afgeleid ≈ she quickly becomes distracted

You could also say:

ze wordt snel afgeleid – she gets distracted easily

Both are natural; raken + participle/adjective is just another pattern Dutch uses to indicate entering a state.

Why is the subject repeated: raakt ze snel afgeleid en verliest ze haar concentratie? Can you leave out the second ze?

In coordinated clauses, Dutch often repeats the subject, especially when there is new information in the second part:

raakt ze snel afgeleid en verliest ze haar concentratie

It is grammatical to omit the second ze:

raakt ze snel afgeleid en verliest haar concentratie

but that is less natural here, because the verb verliest would then feel a bit detached. Repeating ze makes the sentence clearer and more balanced.

So:

with ze repeated: very natural
without ze: possible, but stylistically weaker in this case

Why is it verliest ze haar concentratie and not verliest ze de concentratie or just verliest ze concentratie?

haar concentratie = her concentration (possessive pronoun + noun)
de concentratie = the concentration (more general, not clearly hers)
concentratie verliezen without article sounds odd and incomplete.

Because the concentration clearly belongs to Sofie, Dutch naturally uses a possessive pronoun:

verliest ze haar concentratie

Using de concentratie would sound like some kind of general or abstract “the concentration” in the room, not specifically hers. The possessive haar makes the reference precise and personal.