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