I am new to this game and can't figure out how to get more party slots for battles. I am really struggling to beat the first little boss in the fungus grove with my level 18-19 pet.

Hello! You go to Esior's Haven and to the Sylesti Plaza. Scroll down to where the trainer is. You should be able to buy another party slot, but if not, then you have to wait till you get to Umbra Forest. Hope this helped! I can also send you some relics if you like.

When you are in the world map, click on "Viridian Meadows" (which is probably the only zone open to you at this point I believe?) and then click on "Estior's Haven", which is highlighted purple. Once you're in Estior's Haven, click on "Sylesti Plaza", which is highlighted blue, and scroll down to where it says something about increasing the number of party pet slots. If you don't have enough gold, send me a CoD fee and i'll pay it for you. And here is a pet with pretty ok stats that I found on advanced search that you can use as your second party pet:

If you need any more help lmk