https://www.youtube.com/watch?v=gYePFcTVKIsHere's ~2 minute Enuo and if you're willing to spend ~10 extra seconds you can reduce the RNG failure to succeeding two 80% chance rolls. Sub 2 minutes is possible if everything goes perfectly, i.e. the game picks the least time-wasting actions for Enuo. I think the Steam port is faster (Enuo's intro clearly takes less time on the Steam version) so this strategy is probably a guaranteed sub-2 minutes even with the RNG precautions.
The strategy is as follows:
All Freelancers, wearing Ribbon + Hermes Sandals + your favorite body armour.
Bartz - Masamune + anything else (you just need double digit damage), !Time, !Mix. Aegis Shield can potentially reduce time with RNG.
Everyone else - 2x Dragon Lances, !Aim, !Jump
First you one-cycle Enuo's first form as follows: Bartz !Quicks a regular attack (to get his HP < 599996) and then !Mixes a Dragon Kiss on Enuo. This makes him a Dragon type, which has the effect of making Dragon Lances deal 8x damage that bypasses defense. The Masamune also guarantees this is the first action of the fight. Then everyone !Aims a 9999 damage 2x Dragon Lance. Note that the initial !Quick prevents Enuo's first form from taking a turn and wasting time with an action. !Aim is used because !Mug, !Dance, !Focus and !Jump are the only other abilities that are guaranteed to hit and they all take more time to execute even assuming you get perfect Sword Dances.
For the second form, !Quick isn't needed (you can do it if you absolutely need to reduce RNG reliance but it'll cost time), so Bartz just mixes another Dragon Kiss onto Enuo. Then everyone !Jumps. !Jumps are used this time because Enuo's Protect status reduces the damage from !Aim to ~5-6k. Then Bartz takes a turn to attack Enuo and drop his HP < 59996, and then everyone completes their jumps and Enuo is dead. Note that you can give Bartz an Aegis Shield to potentially speed up the second phase since Enuo will be able to get off a move and a Aegis Shield proc can cancel the animations, but at this point it's just RNG to get those.
Note that technically Bartz can die during the second form if he does something like Almagest/Meteo > Dimension Zero since that actually reach his HP total but like I mentioned in the strategy you can avoid that by using !Quick !Fight !Mix for the second form. If the Dimension Zero counts as a physical attack, then you can also dodge it by giving Bartz a Mirage Vest. In either case, there is a guaranteed way to avoid getting killed so you only need two physical attacks to land for the strategy to work.