Soloing as a pugilist is all about counterattacks. And I don't mean passive counterattacks like other games, this is actively countering enemy actions against you. First off, whenever you dodge an attack, you can use Haymaker, which does a heft amount of damage and inflicts slow. This rewards you both for using Featherfoot to dodge attacks, and for paying attention to your hotbar and not just spamming. Also, at 15 and 30 you get DoT attacks, which require paying attention to the enemy's debuffs so you re-apply them when they wear off, and not before.

In addition, as I mentioned before, while an enemy is readying a special attack is a prime time to circle around it and get a directional bonus. In addition, at level 38 you get the ability Steel Peak, which stuns the monster long enough for you to circle around.

These are all things that make solo combat as a pugilist more than just spamming the same three moves over and over. Getting the bonuses doesn't require a party (though that makes it a lot easier), but if you're solo it's all about paying attention to the fight and reacting accordingly.