I would recommend pronouncing this word with at least four syllables.
When you talk in your question about a pronunciation with three syllables, you seem to be referring to an audio file linked from the Free Dictionary entry. I have never seen a written transcription of the pronunciation of certiorari that showed it as having three syllables.
I prefer to use transcriptions rather than audio files for pronunciation information: transcriptions leave less room for uncertainty and do a better job of indicating the important parts of a pronunciation but not the unimportant details.
Another reason not to use audio files (or to only use them as a supplement to written transcriptions) is that in some cases, they are just wrong. That seems to be the case here. This audio file, which sounds like it was automatically generated/artificially produced, seems to place the primary stress on the first syllable: to me, it sounds something like [ˈsəːʃəri] (rhyming with a certain pronunciation of tertiary). Perhaps whatever software was used to generate it based the pronunciation on the pattern of words ending in -ary (where American English speakers typically have a secondary stress on the -a(r)- while British English speakers leave the vowel corresponding to the letter a fully unstressed and may elide it).
That would be a mistake because certiorari does not end in -ary. In both American English and British English, the primary stress in the pronunciation of certiorari standardly falls on the -ra(r)- syllable, which obviously excludes the possibility of eliding this syllable. The preceding o would normally also correspond to a separate syllable (it's unlikely for the o to be elided because vowels are resistant to elision when they are immediately followed by a stressed syllable). Along with the initial cer(t)- and the final -(r)i, that adds up to at least four syllables. You may choose whether to use a fifth: since the medial -(t)i- is followed by an unstressed syllable, there is the option of eliding the i here.