Tongue pulls back slightly from the D position, blending into R. Sounds close to 'jr'.

Americans pronounce dreadfully as DREHD-fuh-lee (/ˈdrɛdfəli/). In "dreadfully", the "dr" cluster blends into a "jr" sound — a natural American English pronunciation. This is called the DR Sounds Like JR, a hallmark of natural-sounding American speech. It comes out as DREHD·fuh·lee. Stress falls on the first syllable — keep everything else short and quick. You'll hear it in sentences like "The red bedspread had a dreadfully dull design".
Record yourself saying "dreadfully" and play it back. The mic stays on your device — nothing's uploaded.
3 syllables, 8 sounds. Tap a syllable to jump to its row, then explore each sound's mouth shape and how it's made.
Tongue pulls back slightly from the D position, blending into R. Sounds close to 'jr'.

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.

Touch the tip of your tongue to the roof of your mouth just behind your teeth. Add vocal cord vibration as you release.

The textbook way isn't wrong — it's just not how anyone actually says it.
In "dreadfully", the "dr" cluster blends into a "jr" sound — a natural American English pronunciation. /d/ shifts toward /dʒ/ ("j"), so DR sounds like "jr".
In "dreadfully", the "d" is not released — the articulators get into position but hold without the burst of air. Air stops but there's no release burst — the articulators hold position.
Stress falls on the first syllable, not the others. Stretch DREHD — 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.