Can I play Shen 3 energy cost to a battlefield I'm attacking or only I control?

No — you can only play Shen to a location you control (your Base or a Battlefield you control), never to a Battlefield you're attacking.

Shen's [Reaction] keyword only grants timing permission (play during closed states); it doesn't override the placement restriction in his reminder text ("including to a battlefield you control"). When you attack a battlefield, you don't control it, so Shen can't be played there — even in response to the showdown. Defending players, however, can play Shen to battlefields they already control (Rule 355.2; RiftJudge FAQ #8206, #9449).