Who are "bully boys" in sea shanties?

bully, adj comes from the attributive use of the noun "bully" - now obsolete in this sense, except in the phrase "Bully for you" = "Well that is excellent news for you - well done":

OED

bully, n¹

I. A term of endearment and related uses.

†1. a. A term of endearment and familiarity, originally applied to either sex: sweetheart, darling. Later applied to men only, implying friendly admiration: good friend, fine fellow, ‘gallant’. Often prefixed as a sort of title to the name or designation of the person addressed, as in Shakespeare, ‘bully Bottom’, ‘bully doctor’. Obsolete exc. archaic.

?1548 J. Bale Comedy Thre Lawes Nature ii. sig. Biiijv The woman hath a wytt, And by her gere can sytt, Though she be sumwhat olde. It is myne owne swete bullye, My muskyne and my mullye.

1753 S. Richardson Hist. Sir Charles Grandison IV. xv. 115 I haue promised to be with the sweet Bully early in the morning of her important day.

b. attributive, as in bully-boy.

1609 T. Ravenscroft Deuteromelia 6 He that is a bully boy, come pledge me on the ground.

1880 T. E. Webb tr. J. W. von Goethe Faust i. ii. 53 My over jolly bully-boy, let be.

2. dialect. Brother, companion, ‘mate’.

1825 J. T. Brockett Gloss. North Country Words (at cited word) Now generally used among keelmen and pitmen to designate their brothers, as bully Jack, bully Bob, etc. Probably derived from the obsolete word boulie, beloved.

1863 Tyneside Songs 61 Marrows, cries a bully, aw've an idea..We'll find Sir John Franklin.