Kvaliteten af hendes arbejde er så høj, at selv kritikken ikke lyder særlig hård.

Because the noun is specific. The sentence is talking about the quality of a particular thing, namely her work. In Danish, just like in English, that usually calls for the definite form.

So:

• kvalitet = quality, in general
• kvaliteten = the quality

Here, af hendes arbejde makes it specific, so kvaliteten is natural.

Af here means of. The phrase kvaliteten af hendes arbejde matches English the quality of her work very closely.

This structure is very common in Danish:

• slutningen af filmen = the end of the film
• farven af væggen = the color of the wall

You could sometimes express the same idea in other ways, such as with a compound noun, but kvaliteten af hendes arbejde is completely normal and clear.

Because possessive words like min, din, hans, hendes, vores already make the noun definite in meaning. So the noun itself stays in its basic form.

Compare:

• arbejde = work
• arbejdet = the work
• hendes arbejde = her work

You do not combine a possessive with the definite ending here. So hendes arbejdet would be wrong.

This is about Danish reflexive possession.

Sin/sit/sine refers back to the subject of the same clause. But in this sentence, the subject is kvaliteten, not she.

So:

• Kvaliteten af hendes arbejde... = the quality of her work

You cannot use sit here, because sit would have to refer back to the clause subject, and kvaliteten is not something that can possess work.

A useful comparison:

• Hun elsker sit arbejde. = She loves her own work.
• Hun elsker hendes arbejde. = She loves another woman’s work.

In your sentence, hendes is the correct choice.

This is the Danish pattern for so ... that.

• så høj = so high
• at = that
• så høj, at ... = so high that ...

So the sentence builds cause/result:

• Kvaliteten ... er så høj, at ...
• The quality ... is so high that ...

Important: at can mean different things in Danish. You may know it as the infinitive marker, like to in English. But here it is a conjunction meaning that.

Because at introduces a subordinate clause.

The part after it, selv kritikken ikke lyder særlig hård, depends on the first clause. In written Danish, a comma before a subordinate clause is very common.

You should know that Danish allows two comma systems, so you may sometimes also see the sentence without that comma. But the comma here is perfectly normal.

Because selv here means even, not itself.

• selv kritikken = even the criticism
• kritikken selv = the criticism itself

That is an important difference.

In your sentence, the meaning is that the quality is so high that even the criticism does not sound very harsh. So selv kritikken is the right choice.

That is a very common learner question, and the answer is subordinate clause word order.

After at, Danish usually places sentence adverbs like ikke before the finite verb:

• ... at selv kritikken ikke lyder særlig hård

In a main clause, you would normally get:

• Selv kritikken lyder ikke særlig hård.

So:

• main clause: verb before ikke
• subordinate clause: ikke before the verb

This is one of the most important word-order differences in Danish.

Because lyder means sounds. It expresses how something comes across, not necessarily what it objectively is.

So:

• kritikken er hård = the criticism is harsh
• kritikken lyder hård = the criticism sounds harsh

In your sentence, the idea is that even the criticism does not sound especially harsh. That gives a softer, more impression-based meaning.

Because they agree with common-gender singular nouns.

In Danish, predicate adjectives often agree with the noun they describe:

• kvaliteten is common gender singular, so: høj
• kritikken is common gender singular, so: hård

Compare:

• arbejdet er højt vurderet — here arbejdet is neuter, so you often see -t forms in matching contexts
• det lyder hårdt = it sounds harsh
• kritikken lyder hård = the criticism sounds harsh

So the form depends on what the adjective refers to.

Here særlig means particularly or especially.

So:

• ikke særlig hård = not particularly harsh

This is a very common Danish pattern: ikke særlig + adjective/adverb.

You may also come across ikke særligt in similar sentences. Both exist in real Danish usage, but ikke særlig hård is very natural and idiomatic.

Yes, kritikken is definite singular: the criticism.

Danish often uses the definite singular when referring to a specific body of criticism that is understood from context. Here it means something like the criticism she receives or the criticism of her work.

English often just says criticism without an article, but Danish frequently prefers the definite form in this kind of sentence.

So kritikken does not necessarily mean one single comment. It can mean criticism in general within that situation.