To unlock you must simply complete the story mode beating all eight opponents using TJ combo on any difficulty earning any objectives.
If you want progress towards :
He has three objectives, and all can be completed in one run.
1) Beat story mode. Simply win all eight fights.
2) Use an auto barrage on all eight opponents. This is TJ's combo trait, and is activated by cancelling an auto double into a combo utilising all six punch and kick combinations. To get the damage ender required (heavy punch animation) do not follow an Auto with the same strength.
For instance, use LP, MP, HP, LK, MK, HK (
)
Hopefully this helps :
3) Ultra combo Fulgore in the Pinncale. Simply beat Fulgore with an Ultra in the seventh fight. His ultra is
,
+
when Fulgore's health is reading 'danger'.