Hun prøver ikke bare at undskylde, men også at rette sin fejl, så ingen bliver skuffede igen.

Because Danish main clauses usually follow the V2 rule: the finite verb comes in the second position.

So in:

Hun prøver ikke bare at undskylde...

• Hun = subject
• prøver = finite verb
• ikke bare = adverbial part

That is why prøver must come before ikke.

This is different from English, where not often comes directly before the main verb:

• English: She not only tries...
• Danish: Hun prøver ikke bare...

So the placement of ikke here is normal Danish word order.

Ikke bare ... men også ... means not only ... but also ...

In this sentence:

• ikke bare at undskylde = not only to apologize
• men også at rette sin fejl = but also to correct her mistake

It is a very common pairing in Danish, just like in English.

Other examples:

• Han læser ikke bare bøger, men også aviser.
  He reads not only books, but also newspapers.
• Vi vil ikke bare tale om problemet, men også løse det.
  We want not only to talk about the problem, but also solve it.

Because both are infinitives linked to prøver.

• prøver at undskylde
• prøver ... at rette sin fejl

In Danish, at often works like English to before an infinitive.

Here the structure is basically:

• Hun prøver at undskylde
• Hun prøver også at rette sin fejl

When these are combined with ikke bare ... men også, both infinitives keep at.

You may sometimes see at omitted in coordinated structures in informal usage, but here repeating it is clear and standard.

It can mean both, depending on context.

Common uses:

• at undskylde = to apologize
• at undskylde nogen/noget = to excuse someone/something

In this sentence, at undskylde clearly means to apologize.

Related noun:

• en undskyldning = an apology / an excuse

Examples:

• Jeg vil gerne undskylde.
  I would like to apologize.
• Han prøvede at undskylde sin opførsel.
  He tried to excuse his behavior.

So the exact meaning depends on what follows and on the situation.

Because Danish uses sin/sit/sine for a reflexive possessor: when the owner is the subject of the clause.

Here the subject is Hun, and the mistake belongs to her, so Danish uses:

• sin fejl = her own mistake

If you said hendes fejl, it would normally suggest someone else’s mistake, not the subject’s own.

Compare:

• Hun retter sin fejl.
  She corrects her own mistake.
• Hun retter hendes fejl.
  She corrects her mistake = usually someone else’s mistake, belonging to another woman.

This is a very important difference from English, because English uses her for both meanings.

Because the form depends on the gender and number of the noun being possessed.

The noun is fejl, and en fejl is a common gender singular noun.

So:

• sin
  • common gender singular noun
• sit
  • neuter singular noun
• sine
  • plural noun

Examples:

• sin fejl → one common-gender noun
• sit problem → one neuter noun
• sine fejl → plural noun

So sin fejl is the correct form.

Here så means so that or with the result that, not just simple conversational so.

In the sentence:

... så ingen bliver skuffede igen.

it introduces the consequence or purpose:

• she is trying to fix the mistake so that nobody will be disappointed again

Danish så can have several meanings, including:

• so
• then
• such
• so that

Here it is best understood as so that.

Because ingen means no one / nobody, but it can refer to people in a general plural sense, so Danish often uses the plural form of the adjective.

• skuffet = disappointed, singular
• skuffede = disappointed, plural

So:

• ingen bliver skuffede = nobody becomes disappointed / no people are disappointed

This may feel odd to an English speaker, because English does not show this distinction in the same way.

You will often see plural agreement after ingen when the meaning is no people:

• Ingen er perfekte.
  Nobody is perfect.
• Ingen bliver overraskede.
  Nobody gets surprised.

So skuffede is natural here.

Both kinds of structure exist in Danish, but bliver + adjective/participle is very common when describing a change of state.

• bliver skuffede = become disappointed / end up disappointed

This emphasizes the result or state people end up in.

A form like ingen skuffes igen would mean something closer to:

• no one is disappointed again and can sound a bit more formal or more passive in style.

So bliver skuffede is a very natural everyday way to say it.

Igen means again.

It comes at the end because that is a very natural position in Danish for short adverbs of time or repetition, especially after the rest of the clause is already complete:

• ingen bliver skuffede igen

This is similar to English:

• nobody gets disappointed again

Danish often places words like igen, snart, nu, derhjemme, etc. toward the end of the clause unless there is a reason to emphasize them elsewhere.

Yes. In many contexts, prøver can correspond to either tries or is trying in English.

Danish does not always mark the progressive the way English does. So:

• Hun prøver... can mean
  She tries... or She is trying...

The best English translation depends on context.

In this sentence, is trying often sounds more natural in English if you are describing a current situation:

• She is not only trying to apologize, but also to correct her mistake...

But grammatically, the Danish form itself is just the present tense prøver.

Yes. The sentence is very natural Danish.

It uses several extremely common patterns:

• Hun prøver at... = She is trying to...
• ikke bare ... men også ... = not only ... but also ...
• sin for reflexive possession
• så ... for consequence/purpose
• bliver + adjective for becoming something

So even if a learner finds a few parts tricky, the overall structure is standard and useful to learn as a model.