If you're playing WKC1 (from its disc), you're going to have an incredibly difficult time with the S ranks of the high-level quests because they're really that difficult with just your solo character. Beyond that, you'll have an even harder time if you can't unlock the quasi-DLC quests (e.g. Sprog Cleaning) -- and I don't know if you can do that now that the servers are down (and haven't tried) -- because there are barely enough quests to hit the trophy without them.
There are enough reports regarding players getting the WKC1 platinum trophy completely solo/offline that I won't discount the possibility. It's just going to be a lengthy slog, and the quest ranking trophies are by far the hardest part of WKC1's group. On the other hand, I imagine the most difficult part of the WKC2 trophies (solo/offline) will be defeating Vellgander's Apex without a full party because I doubt the AI is going to be particularly adept at that one.