"that may be beaten" in any sense of the verb, 1610s, from beat (v.) + -able.
Entries linking to beatable
beat v.
Old English beatan "inflict blows on, strike repeatedly, thrash" (class VII strong verb; past tense beot, past participle beaten), from Proto-Germanic *bautan (source also of Old Norse bauta, Old High German bozan "to beat"), from PIE root *bhau- "to strike."
Past tense form beat is from c. 1500, probably not from Old English but a shortening of Middle English beted. Of the heart, c. 1200, from notion of it striking against the breast.
The meaning "overcome in a contest" is from 1610s (hence the sense of "legally avoid, escape" in beat the charges, etc., attested from c. 1920 in underworld slang). The sense of "be too difficult for" intellectually or physically (by 1870) is behind the shrug-phrase beats me.
The meaning "strike cover to rouse or drive game" (c. 1400) is the source of beat around (or about) the bush (1570s), the metaphoric sense of which has shifted from "make preliminary motions" to "avoid, evade." The nautical sense of "make progress against the wind by means of alternate tacks" is from 1670s. Command beat it "go away" is recorded by 1906 (though "action of feet upon the ground" was a sense of Old English betan); it is attested in 1903 as newsboy slang for "travel without paying by riding on the outside of a train."
-able
common termination and word-forming element of English adjectives (typically based on verbs) and generally adding a notion of "capable of; allowed; worthy of; requiring; to be ______ed," sometimes "full of, causing," from French -able and directly from Latin -abilis. It is properly -ble, from Latin -bilis (the vowel being generally from the stem ending of the verb being suffixed), and it represents PIE *-tro-, a suffix used to form nouns of instrument, cognate with the second syllables of English rudder and saddle (n.).
A living element in English, used in new formations from either Latin or native words (readable, bearable) and also with nouns (objectionable, peaceable). Sometimes with an active signification (suitable, capable), sometimes of neutral signification (durable, conformable). It has become very elastic in meaning, as in a reliable witness, a playable foul ball, perishable goods. A 17c. writer has cadaverable "mortal."
To take a single example in detail, no-one but a competent philologist can tell whether reasonable comes from the verb or the noun reason, nor whether its original sense was that can be reasoned out, or that can reason, or that can be reasoned with, or that has reason, or that listens to reason, or that is consistent with reason; the ordinary man knows only that it can now mean any of these, & justifiably bases on these & similar facts a generous view of the termination's capabilities; credible meaning for him worthy of credence, why should not reliable & dependable mean worthy of reliance & dependence? [Fowler]
In Latin, -abilis and -ibilis depended on the inflectional vowel of the verb. Hence the variant form -ible in Old French, Spanish, English. In English, -able tends to be used with native (and other non-Latin) words, -ible with words of obvious Latin origin (but there are exceptions). The Latin suffix is not etymologically connected with able, but it long has been popularly associated with it, and this probably has contributed to its vigor as a living suffix.