For example, a Pokemon uses sucker punch on another which uses phantom force. Same applies for fly, dig, dive, solar blade, sky drop... Would the sucker punch fail in the first turn or not?
On both turns, the Pokemon using the 2-turn attack counts as selecting an attack, so sucker punch won't fail. However, using a move like dig often makes sucker punch miss on the second turn, which I'm pretty sure is different from failing. source
No, it will not fail on the first and second turn because you are still attacking the opponent. (unless the two-turned attack has the user disappear like dig or fly.)
