Lexical Definition

‎κράτιστος‎ krátistos (krat'-is-tos) excellent ^G:A
superlative of a derivative of ‎κράτος‎

most excellent (noble).

• strongest, i.e. (in dignity) very honorable

Abbott-Smith

κράτιστος, -η, -ον, superl. of κρατύς (Hom.),
1. strongest, mightiest (Hom.).
2. noblest, best (cf. κρείσσων), most excellent (Pind., Soph., al.): voc., κρατίστε, as title of honour and respect (DCG, ii, 727a), Lk 1:3, Ac 23:26 24:3 26:25.†

Abbott-Smith References

Liddell-Scott-Jones

κράτιστος-ος, η, ον,

Epic dialect κάρτ- (as always in [Refs 8th c.BC+], strongest, mightiest, [Refs 8th c.BC+]; Λημνίων τὸ κ. the best of their men, [Refs] the strength or flower of.., [Refs 5th c.BC+], etc.; of things, καρτίστην.. μάχην fiercest fight, [Refs 8th c.BC+].

__2 generally, best, most excellent, as superlative of ἀγαθός, [Refs 5th c.BC+]; οἱ κράτιστοι the aristocracy, [Refs 5th c.BC+]
__2.b as a title or mode of address, [NT]; especially = Latin egregius, [Refs 1st c.AD+], of a woman of the equester ordo, [Refs] Latin clarissimus, of Senators, ὁ κ. ἀνθὐπατος [Refs 3rd c.AD+]
__2.c with modal words added, [Refs 5th c.BC+]; πάντων πάντα κ. best of all in.., [Refs 6th c.BC+]: with infinitive, best at doing, [Refs 5th c.BC+], etc.: with participle, [Refs].
__3 neuter followed by infinitive, φυγέειν κάρτιστον to flee were best, [Refs 8th c.BC+]: absolutely, ὅπερ κ. the main point, [Refs 5th c.BC+]
__4 adverb usages, ἀπὸ τοῦ κρατίστου in all good faith, [Refs 2nd c.BC+]: neuter plural κράτιστα as adverb, [Refs 5th c.BC+] —The _comparative_ in use is κρείσσων (which see).

_{LSJ Scripture Refs: Luke.1.3}