Flare your lips and lift the mid-front tongue close to the roof of your mouth. Blow air through without voicing.

Americans pronounce shakespearean as shayk-SPEER-ee-uhn (/ˌʃeɪkˈspɪriən/). Stress falls on the second syllable — keep everything else short and quick. You'll hear it in sentences like "He directed a modern adaptation of a Shakespearean tragedy".
Record yourself saying "shakespearean" and play it back. The mic stays on your device — nothing's uploaded.
4 syllables, 9 sounds. Tap a syllable to jump to its row, then explore each sound's mouth shape and how it's made.
Flare your lips and lift the mid-front tongue close to the roof of your mouth. Blow air through without voicing.

Start with your jaw slightly open and the front of your tongue forward and slightly up. Glide upward, your jaw closes a little more and your tongue arches higher toward the roof of the mouth.
Raise the back of your tongue to touch the soft palate (velum). Stop the air, then release.

Place your tongue tip near the roof of your mouth behind your top teeth. Push air through the narrow gap. No voicing.

Press your lips together to stop the air, then release. No vocal cord vibration.

Start with the high 'ih' position. Pull the tongue back and up while flaring the lips slightly.
The textbook way isn't wrong — it's just not how anyone actually says it.
In "shakespearean", the short unstressed vowel before "n" disappears — the schwa is absorbed and the "n" becomes the syllable nucleus on its own. Schwa is absorbed — consonant becomes the syllable nucleus.
Stress falls on the second syllable, not the others. Stretch SPEER — keep everything else short and quick.
Don't pronounce the third syllable too fully. The unstressed syllable reduces to a schwa — the lazy "uh" sound — in casual speech.
Americans use a relaxed retroflex R — the tongue curls back rather than rolling. The R is one continuous sound with the vowel before it, not two separate sounds.