Status Cures are for the weak. I just tanked it. Beat it on the second try when I realised I didn't have enough healing items. You can just target the egg manually and just keep punching it until your special builds up and then use that on it. I did like 4000 damage to the egg with Seraphimon's special.
The weird part is, I chose a different egg each time, almost at random. And I mixed the training up occasionally. But to be honest attack and defense are the easiest stats to train, (since you can time those easily, even on advanced training).
Brain and HP I just have to spam until I win. (Though MP is pretty easy. You just look at what side that doesn't have a bomb next to it has and then find the one with the matching side. Speed is fine too when you realise that sticking to the middle as much as you can allows you to react better to what's coming)
EDIT: I also never made a care mistake. I'm just too paranoid to make them. Even when you intentionally have to. I wanted to get the most out my Digimon's lifespan. (I would of had a Mega in my first generation if it were not for Agumon already being aged when you get him. I had the stats for it.)
So did I, cause I eventually gave away all status cures to make room in the inventory. Its still highly annoying when, besides 3 minutes of running around, you're also stunned or pixelated for an additional 2 minutes inbetween attacks.
And i mean, i beat this boss with a miragegaogamon without any distance attacks on my first try. it took forever cause you barely can land any hits. i spend the first 10 minutes trying to beat the snakes, but by the time i killed the second one (even though it only took one hit per snake) the other one would respawn. they're constantly stopping your attacks with theirs too. very frustrating and yeah, it ended up being mostly waiting for special to fill up and aiming at the cocoon then.
second part was even more annoying since that think kept avoiding my attacks.
as for the minigames, heres a tip for 3d maze. you start, of course, from the bottom of the game and make your way up to the right number. once you get an eye for identifying the exit without a bomb, things will get much easier.
also, you can speed up your line following a lot if you realize that an even number of lines in a row means you stay on the same vertical line. (see upload)
for me, the only times i come close to failing on that game now, even on advanced, is if the line is constantly moving up like a spiral. like 1>2>3>1>2 etc, because then i need to follow every line 'manually' and sometimes run out of time to select the right answer.
the hp one, you can only do so much, but just always aiming for the 7 is a must. you always know where the seven is and if you can get the beat down for when the wheel makes one revolution, it gets much easier. i still prefer to keep it to intermediate for this one most of the time though, since advanced is just too hit and miss and I have to save between every single train just to make sure and that takes so much time.
as for your agumon, I'm pretty sure i've read of people getting megas on their first digimon, you sure you weren't going for something that required unlocking first? (i made that mistake too) wargreymon, dukemon, beelzemon, and a bunch of others only work once you unlock them.