Learn French: Le batteur travaille dur pour cet enregistrement. - The drummer works hard for this recording.

In French, certain adjectives are used directly as adverbs with specific verbs. With travailler, we use dur to mean "hard" (putting in a lot of effort). Because dur is acting as an adverb modifying the verb here, it is invariable. This means it will never take an -e or an -s, even if the subject is feminine or plural (for example, les batteuses travaillent dur).

Since the lesson includes parler fort, could I say le batteur travaille fort?

In standard European French, travailler dur is the fixed expression for "working hard." Travailler fort is commonly used in Canadian French, but elsewhere you should stick to travailler dur. Save fort for expressions like parler fort (speaking loudly) or frapper fort (hitting hard).

Why is it cet enregistrement instead of ce enregistrement?

Enregistrement (recording) is a masculine singular noun. Normally, you use ce for masculine nouns to mean "this" or "that." However, because enregistrement starts with a vowel, ce changes to cet to avoid a harsh gap in sound between two vowels. If the noun were plural, it would just be ces enregistrements.

How does the word relate to the actual drum set?