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.

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
'zerstören' and 'zertrümmern' both mean that something is damaged very severely. 'zerstören' is more general: a house, a device, a plan, or a relationship can be destroyed. 'zertrümmern' sounds stronger and more concrete. It fits especially when something is smashed into many pieces with great force, for example glass or stone. In a figurative sense, 'zertrümmern' sounds more dramatic than 'zerstören'.

Beim Unfall wurde die Windschutzscheibe vollständig zertrümmert.
The windshield was completely shattered in the accident.
Der Sturm hat mehrere Häuser am Fluss zerstört.
The storm destroyed several houses by the river.