Much like Danmaku said, this is probably not possible with how the hunt is designed, but a highly skilled hunter and with overpowered stats, it may be possible to at least reach the lava cavern phase.
For weapon, you are going to want a fire weapon with part breaker 3 and affinity built. Fire helps the armor go into the molten state much faster, making it easier to break.
The first phase of the hunt is very easy to advance, even solo. Just make sure you land every fallen boulder on taroth and she'll move to the cavern at level 1.
The cavern fight is where things get iffy. You need to do considerable damage and break enough parts in order to move to the lava cavern. You can build for flight and use the jump mantle to help with this and at least get the horn plating off. Keep using fire and part breaker.
If you can get to the lava cavern, good job. go back to camp and switch your weapon to something harder hitting (fire could still work, but there are better weapons). You have to rely on the environment if you have any hope of progressing to the final fight. If you don't land all three boulders and have her in an eruption. You will not move on. In order to move on to the final battle, you must knock off Taroth's armor entirely, by doing a very large amount of damage. Not possible for a single player, unless you have a broken build and hit every environmental hazard.
If, by some miracle you fit the broken build criteria and get Taroth to the final fight. You need 2 things: a weapon with partbreaker, and skills for easier and more often mounting. Knock her down and bomb her horns as often as you can and keep the damage going (anywhere, not just horn... to trigger knockdowns).
So, it's likely not possible to clear it at pursuit 1... even with this guide. This guide, though, will get you far enough that the next run will be pursuit 3 or 4, which is definitely soloable.