Act half-heartedly boxing fighter, old one like Achilles? (7)
I believe the answer is:
demigod
'one like achilles?' is the definition.
'demigod' can be an answer for 'achilles?' (thesaurus). I'm not certain of the 'one like' bit.
'act half-heartedly boxing fighter old' is the wordplay.
'act half-heartedly' becomes 'ded' (I am not sure about this - if you are sure you should believe this answer much more).
'boxing' is an insertion indicator ('box' can mean contain, as in to put in a box).
'fighter' becomes 'mig' (fighter jet produced by Russian company MiG).
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'mig'+'o'='migo'
'ded' enclosing 'migo' is 'DEMIGOD'.
Can you help me to learn more?
(Other definitions for demigod that I've seen before include "A partly divine being" , "His nature is only partially divine" , "Half-divine person" , "Half-deity" , "Part mortal, part deity" .)