hellwach
wide awake
Physically completely awake and not tired at all.
Nach dem starken Kaffee war ich plötzlich hellwach und konnte die ganze Nacht arbeiten.
After the strong coffee, I was suddenly wide awake and could work all night.

wide awake / alert
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wide awake
Physically completely awake and not tired at all.
Nach dem starken Kaffee war ich plötzlich hellwach und konnte die ganze Nacht arbeiten.
After the strong coffee, I was suddenly wide awake and could work all night.

The word consists of 'hell' (bright) and 'wach' (awake). Here, 'hell' acts as an intensifier and means 'entirely' or 'completely'. Someone who is 'hellwach' (wide awake) is therefore absolutely no longer tired.
Das laute Geräusch machte mich mitten in der Nacht hellwach.
The loud noise made me wide awake in the middle of the night.
'Hellwach' (wide awake/alert) is mostly used predicatively with verbs like 'sein' (to be), 'werden' (to become), or 'bleiben' (to remain). It can also describe the manner of an action as an adverb.
Trotz der späten Stunde war der Student noch hellwach.
Despite the late hour, the student was still wide awake.
When referring to being physically awake, the word is often used in situations where one should actually be sleeping. Typical phrases are 'die ganze Nacht hellwach liegen' (to lie wide awake all night) or 'plötzlich hellwach werden' (to suddenly become wide awake).
Wegen meiner Sorgen lag ich die halbe Nacht hellwach im Bett.
Because of my worries, I lay wide awake in bed half the night.
The meaning 'mentally attentive' can often be recognized from the context. If it is about sports, a dangerous situation, a discussion, or an intellectual task, mental alertness is usually meant.
Ein guter Autofahrer muss immer hellwach sein und schnell reagieren können.
A good driver must always be alert and able to react quickly.
attentive / considerate
'aufmerksam' and 'hellwach' can both mean that someone is mentally focused. You use 'aufmerksam' when someone listens, watches, or follows something carefully. 'hellwach' is stronger: the person is not tired at all and reacts quickly. It can be meant physically, as in really awake after sleeping, or mentally very clear. Learners may confuse the words because both have to do with concentration. As a practical rule: 'aufmerksam' fits concentration on something, while 'hellwach' describes the person's awake and quick state.

Nach dem Kaffee ist Tom wieder hellwach und kann weiterarbeiten.
After the coffee, Tom is wide awake again and can keep working.
Während der Besprechung hört die Mitarbeiterin aufmerksam zu.
During the meeting, the employee listens attentively.