Humble yourselves therefore (ταπεινωθητε ουν). First aorist passive imperative of ταπεινοω, old verb, for which see Matthew 18:4. Peter is here in the role of a preacher of humility. "Be humbled."

Under the mighty hand of God (υπο την κραταιαν χειρα του θεου). Common O.T. picture (Exodus 3:19; Exodus 20:33, etc.).

That he may exalt you (ινα υψωση). Purpose clause with ινα and first aorist active subjunctive of υψοω. Cf. Luke 14:11; Philippians 2:9.

In due time (εν καιρω). Same phrase in Matthew 24:45.