I managed to beat 0.8 with just Syle in the Soulstice House with Enburn as her first spell. It's definitely a challenge to fight with just Syle due to the game's formations being suited with 3-4 party members in mind. Here are my experiences on it:

• Combat Basics (both visits) are doable though the Fire Spirit can be difficult depending on what spells Syle has.
• Aura Breaks starts getting difficult as the enemies there can easily defeat Syle. Level grinding to around grade 8 is needed to defeat the Ogres who can be difficult since they have two attacks that stun Syle. I used the Golems to level grind using Enaqua which Syle can learn from Spellcasting: Basics (using the Provision option) or completing Lost Book. If Syle doesn't Alyssa and/or Ein when reaching the bridge, the game will skip the battle.
• The Fairy Forest is doable since you have Uni who can easily defeat the fairies. The Fairy Clip is helpful even though it only gives 50 MP rather than 100. The Earth weakness is not a downside since no enemies as of 0.8 (probably except the Gnome) use Earth attacks. Breaking the crystal may be helpful due to the two items but I didn't break the crystal in my playthrough.
• The Headmaster is nothing different in a soloist run. It can be challenging but anything Snofawks is weak against should work. Using Enaqua should be avoided.
• The third visit to Arashya Forest can be challenging since the Buraflux and Venoflower will initially outspeed Syle and the latter has poison attacks. A good way I level grinded is to use the two Buraflux encounters in the map east of the save point, and using Guard, Enheal, and Strafe. It will take a lot of battles to get Syle to Grade 15.
• First Mission to defeat the Garuda requires getting Syle to around Grade 15. I couldn't use the Enheal Crystal since the Garuda will otherwise stun and kill Syle. The issue would be the Poison Feather which poisons Syle, and Double Peck and Talon Slash which can do a lot of damage. Saving before the battle and using Health Potions will help.
• The Buraflux fight in the Exam didn't seem difficult at Grade 17. I just used Strafe and Senburn to defeat them.
• The Paslime and two Slimes is similar to the Garuda fight. After killing the two Slimes, it's probably easier than the Garuda since the Paslime doesn't have a followup attack and doesn't hit him/her twice. Toxic Sludge can be a problem due to poison but using Health Poisons will help.

The other issue would be the obstacles that require spells or shards. Since Syle can only get two elemental spells (one from Spellcasting: Basics and the other from completing/failing Lost Book), one of them will require a shard. In my playthrough, I started with Enburn and learned Enaqua from completing Lost Book. Enheal can be obtained from the Trader but you can get the Enheal Crystal.