Press your lips together, add vocal cord vibration, then release.

Americans pronounce breathless as BREHTH-luhs (/ˈbrɛθləs/). Stress falls on the first syllable — keep everything else short and quick. You'll hear it in sentences like "The myth of the moth caused a breathless death".
Record yourself saying "breathless" and play it back. The mic stays on your device — nothing's uploaded.
2 syllables, 7 sounds. Tap a syllable to jump to its row, then explore each sound's mouth shape and how it's made.
Press your lips together, add vocal cord vibration, then release.

Curl or bunch your tongue without letting the tip touch the roof of your mouth. Brace the sides of your tongue against your upper back teeth, and round your lips slightly.
Drop your jaw moderately. Touch the tongue tip behind the bottom front teeth and lift the mid-front part slightly toward the roof.

Place the very tip of your tongue slightly between your teeth. Blow air gently around it without voicing.

Place the tip of your tongue against the alveolar ridge just behind your top front teeth, the same contact point as /t/, /d/, and /n/. The difference is what happens to the air: for /l/, you let it flow continuously around the <em>sides</em> of the tongue (that's why /l/ is called a lateral). Turn your voice on the whole time. Lips stay relaxed, no rounding or flaring. For the Dark L variant at the end of a syllable, also pull the back of the tongue up and back toward the soft palate.

Relax your lips, jaw, and tongue completely. Drop your jaw slightly and keep the tongue neutral.
Place your tongue tip near the roof of your mouth behind your top teeth. Push air through the narrow gap. No voicing.

The textbook way isn't wrong — it's just not how anyone actually says it.
Stress falls on the first syllable, not the others. Stretch BREHTH — keep everything else short and quick.
Don't pronounce the first syllable too fully. The unstressed syllable reduces to a schwa — the lazy "uh" sound — in casual speech.