
zucken
to twitch
To make a short, quick, uncontrolled movement of a muscle or body part, often as a reaction to a stimulus, nervousness, or exhaustion.
Sein Augenlid begann unkontrolliert zu zucken.
His eyelid began to twitch uncontrollably.
to twitch / shrug / flash
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to twitch
To make a short, quick, uncontrolled movement of a muscle or body part, often as a reaction to a stimulus, nervousness, or exhaustion.
Sein Augenlid begann unkontrolliert zu zucken.
His eyelid began to twitch uncontrollably.

to shrug
To briefly raise and lower the shoulders to express that you don't know something, don't care, or can't do anything.
Auf die Frage, wo das Geld sei, konnte er nur mit den Achseln zucken.
When asked where the money was, all he could do was shrug.

to flash
To move briefly and quickly as a bright flash of light, especially with lightning.
In der Ferne zuckten Blitze über den Nachthimmel.
In the distance, lightning flashed across the night sky.
The meaning of 'zucken' depends strongly on the subject of the sentence. If a body part is the subject, it means 'to twitch'. If a person 'mit den Achseln' zuckt, it means 'to shrug'. If 'Blitze' (lightning flashes) is the subject, it means 'to flash'.
Sein Mundwinkel zuckte nervös.
The corner of his mouth twitched nervously.
In the meaning 'to move uncontrollably', 'zucken' (to twitch) is often used with certain body parts. Typical examples are: 'das Augenlid zuckt' (the eyelid twitches), 'der Muskel zuckt' (the muscle twitches), or 'der Mundwinkel zuckt' (the corner of the mouth twitches).
Wenn ich müde bin, zuckt mein linkes Augenlid manchmal.
When I'm tired, my left eyelid sometimes twitches.
The expression 'mit den Achseln zucken' (to shrug one's shoulders) is a fixed unit. It expresses that someone doesn't know an answer, doesn't care about something, or is helpless.
Als ich ihn nach dem Weg fragte, zuckte er nur mit den Achseln.
When I asked him for directions, he just shrugged.
to tremble
Both words can describe an involuntary movement caused by nervousness. „Zittern“ usually describes a continuous, rapid movement, while „zucken“ refers to a brief, single movement of a muscle or body part. For prolonged trembling, „zittern“ is appropriate; for a short jerk, „zucken“ is more suitable.

Vor Nervosität zuckte ihre Hand einmal kurz.
Her hand twitched briefly once from nervousness.
Vor Nervosität zitterte ihre Hand während des ganzen Gesprächs.
Her hand trembled with nervousness throughout the conversation.