The first thing I would like to point out is that this build may take a few runs to fully get. As the skills that you recieve and amount of bugs that you find isn't static. But if you get the mage build going, then you are almost sure to win unless you die from biome traps.

First off you want to have the mage hat unlocked as well as the remnant class. The synergy from those works well with this build, but its not mandatory. If you don't have the remnant class then others will work, its just that your magic won't be as high as it could be. Plus the remnant are the only ones who start off with a staff, so any others will rely on you finding the bugs and having a net to get them. Next, for the trait that you will want to start with is potion brewer for certain as you will need mana pots if you don't get the clairvoyance skill. As for the second trait, that one is up to your preference. You can opt for more attack, health, or grab gatherer in hopes of getting more herbs and shrooms. As for your core stats, of course you will want to have 4-5 health, 3-5 attack to help with early kills when mana is low, at least 3 dex, and ideally magic should start off at 4-5.

From there it is a matter of running through biomes in search of spider webs to make a net so you will be able to make a fire staff and lightning staff (if you didn't have the remnant class). As you level you will want to grab mage class skills of course, the best being clairvoyance as this allows spammiing of fireballs. Which go through walls and can hit pretty hard as your magic goes up. The second skill you would hope to get is the minion skill as this will effectively double your damage when facing the final boss, and help with clearing enemies from a safe distance when low on mana. As for a third skill, levitate is nice to have to help you get around traps and dodge enemy projectiles.

Assuming you get all these skills and have a fireball staff by the time you reach the end boss, then the rest is quite simple. Run far enough right from the boss that his projectiles disappear before they reach you and just spam your fireball and minion as often as possible. Clairvoyance should see to it that your mana doesn't deplete, but if it does then thats what your large mana pots are there for. And after a minute or so of fireballs the boss is dead and you are left with a victory screen :). If you didn't have clairvoyance then the same strategy will work as long as you have been saving your mana pots for the boss and just running through the lesser biomes. If you have any questions about this guide, feel free to ask.