Is based on the Greek, Hebrew, or Aramaic text.
Was (preferably) published in the last 40 years or so.
Has a large bibliography and footnotes.
Often has a translation of the original text.
Focuses on narrower areas of the text (such as a book or a few books that can be grouped together, such as the Johannine Epistles).
Tends to have a significant portion of their text devoted to behind-the-text issues such as the composition of the book, history of interpretation, text-critical issues, etc. These issues can have their own chapter.
Examples of critical commentaries include:
The Anchor Bible Commentary series or the Anchor Yale Bible Series (AYBC)
Word Biblical Commentary (WBC)
The Interational Critical Commentary Series (ICC)
The New Cambridge Bible Commentary (NCBC)
The New International Commentary on the Old Testament (NICOT)
The Old Testament Library Series (OTL)
The New Testament Library Series (NTL)
Pillar New Testament Commentary (PNTC)
The Baker Exegetical Commentary on the New Testament (BECNT)
The New International Greek Testament Commentary (NIGTC)
The New International Commentary on the New Testament (NICNT)
This is in contrast to commentaries based on the English text and homiletical and/or devotional commentaries (such as Interpretation, Teach the Text, or The Old/New Testament for Everyone) which would NOT be considered critical commentaries.