mühsam
arduous
Involving great effort, exertion, or patience; difficult or time-consuming.
Der Aufstieg auf den Berg war mühsam, aber die Aussicht hat sich gelohnt.
The climb up the mountain was arduous, but the view was worth it.

arduous / tedious
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arduous
Involving great effort, exertion, or patience; difficult or time-consuming.
Der Aufstieg auf den Berg war mühsam, aber die Aussicht hat sich gelohnt.
The climb up the mountain was arduous, but the view was worth it.

The adjective 'mühsam' (arduous / tedious) is derived from the noun 'die Mühe' (effort). The ending '-sam' means something like 'full of'. So 'mühsam' literally means 'full of effort'.
Das war eine mühsame Aufgabe, aber jetzt ist sie fertig.
That was a tedious task, but now it's finished.
In its main meaning, 'mühsam' often describes physical or mental efforts. Typical nouns are 'Arbeit' (work), 'Aufgabe' (task), 'Weg' (path/way), or 'Suche' (search).
Die Suche nach der verlorenen Brieftasche war lang und mühsam.
The search for the lost wallet was long and arduous.
As an adverb, 'mühsam' describes how an action is carried out: slowly and with a lot of effort. It then stands directly with the verb.
Der alte Mann bewegte sich mühsam die Treppe hinauf.
The old man moved laboriously up the stairs.
Colloquially, 'mühsam' can also describe a person or situation that you find annoying or complicated. This use is informal and slightly negative.
Ein Gespräch mit ihm zu führen ist mühsam, er hört einfach nicht zu.
Having a conversation with him is tedious; he simply doesn't listen.
heavy / difficult
'schwer' and 'mühsam' both describe something that does not go easily. 'schwer' mainly says that something is difficult or demanding. 'mühsam' puts more emphasis on the effort, patience, or long duration involved. A task can be 'schwer' because you have to think a lot. Work is 'mühsam' when it progresses slowly and costs a lot of energy or patience. 'mühsam' often sounds a little like annoyance or exhaustion.

Das Ausfüllen der vielen Formulare war mühsam und dauerte den ganzen Vormittag.
Filling out all the forms was tedious and took the whole morning.
Für Aylin ist der Text schwer, weil viele neue Wörter darin stehen.
For Aylin, the text is difficult because it contains many new words.