For soloing unfair past chapter 1 you'll need:
1. An answer for everything skill wise. Strength/Dex checks, trickery, persuasion, arcana, magic device (for out of school scrolls/wands), perception, etc.
2. An answer to everything combat wise. Dealing with physical hitters, trash encounters, area lockdown or CC in general, stat drains/damage, swarms, AoE damage.
3. To solve weight issues since you're just one member.
4. A way for taking the least amount of time per rest because Time issues.
5. To be able to survive surprise rounds, huge hits (sneak attack/crits) and spells along with fast movement speed without expending spell slots.
A spell caster druid answers everything.
1. Strength and Athletics checks are answered by your Mastodon/Animal Companion when available. Everything else you can comfortably stack up. There are very few feats that actually help a spellcaster druid, so you can afford to get skill related feats and spell focus feats.
2. Physical Hitters are dealt with by making your animal companion buff up, trash encounters are solved by low level spells with the animal companion, alot of CC (Sirocco, spike stones, entangle, cave fangs, etc.), Stat drains/damage (sirocco, plague cloud, creeping swarm) and AoE damage.
3. My Mastodon boosts my carry limit to 2500+ which is more than enough.
4. Druid have every cure wounds tier including Heal itself making you not spend a ton of time just healing.
5. A Druid with Huge Elemental wild shape has DR10/-, +natural AC, +6 to a few stats, immune to sneak attacks and crits, and a lot of movement bonus when using Fire/Wind. For the surviving elements part, the druid has access to both Resist Energy and Protection from Energy spells along with Stoneskin.
With the Feyspeaker archetype, you have more answers to everything. Heroism, invisibility, Crushing Despair (Will negate, -2 to all saving throws, huge monsters likely don't have huge WIS), mirror image, displacement, etc. at the cost of having wilshape later but the only wildshapes that matter are the Elemental ones.
You will have access to Haste, Mage Armor, Shield, wands, etc. due to Magic Device too. Feyspeaker uses Charisma so they have a boost in this skill.
You can clear up Tutorial + Olegs on unfair with a specific druid setup along with making everyone in your initial party (after tutorial basically) have a mastodon for the Oleg's fight. But why would you torture yourself for like 2% of the game, a druid with a good stat spread using a Mastodon can comfortably go clearing Challenging at the start, then hard then soloing unfair for the rest of the game before even the whole kobolds/mytes quest.
I can't say for certain if it will hold up until the very end on Unfair, and hearing about the tomb makes me think. But we'll see, everything up till now (Mid chapter 3) is pretty fine.