I think this seasonal challenge is unnecessarily annoying and grindy to complete because it only counts foes in the overland area.
Foes in Delves or the Public Dungeons (where they're concentrated) don't count. I'm not sure whether killing people in Orsinium counts, I have not tested it.
Also: "foe" is doing a lot of work. If you kill a deer, i.e. do one point of damage to it, that counts as a foe.