A spear can get A or S (the rank needed for blue items) on most quests, but even as a spear the ones below are likely impossible to get A or S:
RoE2 (time limit and difficulty)
WF2 (quest items)
EM2 (damage output too low)
FoW2 (time limit)
QwK2 (time limit)
In terms of gear, anything requiring vessels and the guild shop is out. While other stuff is in the realm of possibility, you can well eliminate the following sets:
whatever uses em2 blues
Regarding the accessory sets, georamas can be visited offline... but would the coins be available in the shop offline?
Long story short, it will not be fun to get the top gear sets in this game by legitimate means in offline mode.