
zertrümmern
to smash
To break something into many small pieces with great force; to destroy it completely.
Der Hagelsturm hat das Glasdach des Wintergartens zertrümmert.
The hailstorm smashed the glass roof of the conservatory.
to smash / shatter
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to smash
To break something into many small pieces with great force; to destroy it completely.
Der Hagelsturm hat das Glasdach des Wintergartens zertrümmert.
The hailstorm smashed the glass roof of the conservatory.

to shatter
In a figurative sense, to completely destroy something abstract, such as hopes, plans, or illusions.
Die schlechte Nachricht zertrümmerte all seine Träume von einer gemeinsamen Zukunft.
The bad news shattered all his dreams of a future together.
The prefix 'zer-' always means that something breaks or falls apart into pieces. Verbs with this prefix are always inseparable, meaning 'zer-' stays attached to the verb in all sentence forms.
Er war so wütend, dass er sein altes Handy zertrümmerte.
He was so angry that he smashed his old phone.
In its literal meaning, 'zertrümmern' (to smash) is often used with hard, breakable objects. Typical objects are glass, a window, furniture, or even bones.
Bei dem Unfall wurde die Windschutzscheibe des Autos zertrümmert.
In the accident, the car's windshield was smashed.
In the figurative sense, 'zertrümmern' (to shatter) is used for abstract things. Common combinations are 'Hoffnungen zertrümmern' (to shatter hopes), 'Träume zertrümmern' (to shatter dreams), or 'Pläne zertrümmern' (to shatter plans).
Die Absage der Universität hat ihre Hoffnungen auf einen Studienplatz zertrümmert.
The university's rejection shattered her hopes of getting a place to study.
to destroy
Both words can mean that something is completely destroyed. Zerstören is the neutral, general term, while zertrümmern emphasizes smashing something particularly forcefully into many small pieces. Use zertrümmern when the violent manner of the destruction should be clearly visible.

Der Bagger zertrümmerte die alte Mauer am Grundstück.
The excavator smashed the old wall on the property to pieces.
Der Bagger zerstörte die alte Mauer am Grundstück.
The excavator destroyed the old wall on the property.