The connection between the adjective anspruchsvoll and the phrase in Anspruch nehmen lies in their root der Anspruch, which means "claim" or "demand."

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In Anspruch nehmen generally means "to make use of" or "to claim." It is often used in contexts of utilizing a service, claiming a right, or demanding something. It means to take advantage of something, but it does not imply any bad intentions.

Diese wurde allerdings nie in Anspruch genommen.

It, by the way, was never laid claim to.

Caption 39, Bundespräsident Wulff tritt zurück: Kredit- und Medienaffäre

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Viel zu lange hat eine kleine Gruppe in Washington die Vorteile der Macht in Anspruch genommen.

For much too long, a small group in Washington has reaped the rewards of power

Caption 23, Tagesschau: Amtseinführung von Donald Trump

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Trotz übersichtlichem Gelände muss auch diese Skifahrerin den Hubschrauber in Anspruch nehmen.

Despite the clear terrain, also this female skier has to make use of the helicopter.

Captions 45-46, Rettungsflieger: Im Einsatz

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The adjective anspruchsvoll describes someone or something that has high demands or expectations. It's worth noting that it can sometimes have a slightly negative connotation, implying that someone is hard to please or overly demanding. However, it can also be used positively to describe something of high quality.

Endspielstrategie oder Endspieltechnik ist auf ihre eigene Art sehr anspruchsvoll.

Endgame strategy or endgame technique is very demanding in its own way.

Caption 36, Schach: Regeln, Strategie und Taktik

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Aber dadurch, dass ich hauptsächlich auf der Ostsee unterwegs bin, wo die Bedingungen sehr anspruchsvoll sind...

but due to the fact that I'm mostly out on the Baltic Sea where the conditions are very challenging...

Captions 26-27, Die Insel Fehmarn: Speedsurfen auf Fehmarn

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You may also see anspruchsvoll translated as "exacting," "sophisticated," or "ambitious."

Further Learning
You'll find more examples on Yabla German. For in Anspruch nehmen, practice writing your own sentences.