Farrington (2012), no. 1.23 and p. 106-9 note 222 offers a detailed reconstruction of Euthymenes' career based off three of Pindar's odes, viz. Nemean 5 and Isthmian 5 and 6, as well as their scholiasts. It goes too far to recount all this here; let it suffice that I have followed Farrington's conclusions with regards to dating and victories. It is a complicated discussion, down to the proposed interpunction and possible omission in the aforementioned odes; Farrington concludes that Euthymenes won two Isthmian and a Nemean victory in the pankration within the given date limits; it is recommended to read his discussion of the sources.
Phylakidas, subject of Isthmian odes 5 and 6, and Pytheas, subject of Nemean ode 5, were Euthymenes' nephews according to Pi. I. 6.62. - PK
The imagery of Nem. 5.43 suggests that Euthymenes’ discipline could also have been some track event. His victory at the Nemea may have occurred in 483 or 481 BC. Euthymenes probably also won in sets of games at Aigina and Megara. - EK