таинственный (mystical) – tainstvennyy – tie-EENST-vyin-nih
загадочный (enigmatic) – zagadochnyy – zah-GAH-dahtch-nih
непостижимый (inconceivable) – nepostizhimyy – nyi-puss-tyih-ZHEE-mih

Because the final syllable is unstressed, many endings for case and gender would be pronounced close enough to "ih".

LONG ANSWER:

The Cyrillic alphabet is very similar to the Roman alphabet. You’d have an easier time learning it than you might guess. If you want to study Russian, transliteration will be a large handicap, the sooner you dispense with it the better.

These three words can mean the same thing as "mysterious" in Russian:

таинственный (mysterious, mystical), загадочный (mysterious, enigmatic), непостижимый (mysterious, inconceivable)

See the letters т, а, е, о and м? They look just like their English counterparts, with т and м pronounced identically. The other letters (а, е, о) are pronounced ah, yeh, and oh respectively in stressed syllables. In unstressed syllables, "а" is pronounced "ah" the syllables next to the stressed syllable and "uh" in other syllables, "е" is pronounced "yih", and "о" is pronounced exactly as though it were "а".

The letters и, й, с, в and н have some semblance with u, ŭ, c, B and H. In French, u represents a rounded "ee" sound, this is close to Russian where it represents an unrounded "ee" sound. (Greek υ is pronounced like Russian и and is the Cyrillic letter’s origin.) The letter с is like English c in practice or city, although it is always soft and corresponds to "s" in English. Russian н can be thought of as an N with the oblique line "corrected" and made perpendicular with other two lines. This letter corresponds with English "n".

The letters п, г, and д are equivalent to Greek Π (pi), Γ (gamma), and Δ (delta) and correspond to English "p", (hard) "g" and "d" respectively. You may have used these letters for abbreviations in your mathematics and science classes.

Finally, з, ч, ж, and ы might be the least familiar to you. However, з looks like some cursive z’s with a tail on the bottom (ʒ), this letter corresponds to English "z". The letter ы is a compound of ъ (the hard sign, which has no pronounciation alone) and I which is no longer a letter by itself in Russian, this letter is pronounced like i in English "bit". The other two letters are uniquely Cyrillic, ч corresponds to English ch (as in church) and ж to English zh (like s in measure, a voiced sh sound).

Now, I can transliterate таинственный; загадочный, непостижимый with a clean conscience.

таинственный – tainstvennyy – tie-EENST-vyin-nih
загадочный – zagadochnyy – zah-GAH-dahtch-nih
непостижимый – nepostizhimyy – nyi-puss-tyih-ZHEE-mih

Since, the pronunciation of a vowel depends on where the stress is in the word, transliteration isn’t sufficient for proper pronunciation, you must know the stress of a word.

tayinstvennyi – masc.