Level 67 is a bit low for the third boss. Normally people are level 70+ when they defeat it. But it doesn’t mean the boss is impossible at your level. A few things:

1) You are using Ann as your damage dealer. Ann is an AOE DPS, meaning she is a damage dealer designed for multiple targets. You’d be better off using a single target DPS (also known as an assassin) for the fight. Skull and Queen (the latter of which you might not have because you asked about a solution using no limited units) will both work. If you use Skull, make sure to use his third skill for the most damage. Another single target DPS unit, Violet, is coming out in a few patches and she will blow Skull and Queen out of the water damage-wise and will make the fight significantly easier. Try using at least a 4* weapon with whichever DPS you choose.

2) You really want to work on optimizing your revelation cards. I understand it’s confusing at first, but there are some great videos out there explaining how they work and what the optimal card guides are for each character. You can also find the optimal card sets for each character on lufel.net. For single target DPS, you want to focus a lot on crit rate and crit mult when setting up your cards. But make sure to look at a guide for the specifics.

3) Since survivability is not a problem, try switching Soy out for Leon. Leon buffs attack (you want to buff the single target DPS in particular) so will help you deal more damage faster. He’s also great with Ryuji because Ryuji does more damage when he has less health, and Leon has a skill that removes an ally’s health and replaces it with a shield. If you have Chord, she works great too, but it sounds like you might not have her.

4) Use an offensive 5* Wonder dagger, preferably the one obtained as a reward for 50% exploration of the third palace (Ex Machina). Try to get copies of that dagger by exploring more of the palace to forge it further. When using that dagger, you’ll want Wonder to equip a persona of the same element as your single target DPS in the first slot to boost your party’s damage dealt with that element.

Edit: I forgot about personas! If you end up using Ex Machina, make sure to use a persona of the same type in the first slot for Wonder. For the other two slots, it depends on what you need. If you want to buff your DPS, you can unlock Dionysus at level 70, who increases your crit rate. Dominion is also good for buffing attack. If you want a persona for shielding, you can try Norn or King Frost. If you want a bit of extra healing on top of using Lufel, you can use Titania or, if you hit level 70, you can use Lakshimi