What does Boxing Day have to do with boxing?
"in any way," mid-14c., originally used only affirmatively (cf. I Sam. XX:6 in KJV: "If thy father at all misse me"); now it is overwhelmingly used only in the negative or in interrogatory expressions, or in literary attempts at Irish dialect.
Old English eall "all, every, entire," from Proto-Germanic *alnaz (cf. Old Frisian, Old High German al, Old Norse allr, Gothic alls), with no certain connection outside Germanic.
Combinations with all meaning "wholly, without limit" were common in Old English (e.g. eall-halig "all-holy," eall-mihtig "all-mighty") and the method continued to form new compound words throughout the history of English. First record of all out "to one's full powers" is 1880. All-terrain vehicle first recorded 1968. All clear as a signal of "no danger" is recorded from 1902. All right, indicative of approval, is attested from 1953.