I made a Yoshitsune once, after laughing banana mention it...
Not sure about invincible.
If I had made that, I wouldn't be rocking my level 85 Trumpeter as default, I'd wager.
Details, please?
SLink MAX trophy is one playthrough (they don't carry) and sort of a pain, even with a guide -- I'm using one, but I'm already making several deviations and hoping they pay off (the guide was written for someone who hadn't maxed all the traits like courage, so I'm doing some things like skipping the jobs that increase those and trying to do nanako/dojima SLinks in their place... it's funny because I'm in June and nanako's SLink 7 was supposed to occur in October in the guide and I already have it. I've been holding off on reading books until I can get the hyper speed reading book again in August...)
Another side note I forgot to mention above -- since you carry money and Daidara's stock over to NG+, you can buy the same weapons/armor you had from the end of your last run IMMEDIATELY pretty much. I have MC/Chie/Yosuke/Yukiko all running with the top weapons i had and top armor. It's amusing like you wouldn't believe. Pretty much everything dies in 1 hit.
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This reminds me -- heckmanimation -- if you want to play P4G but don't feel the need to be challenged by the battles and don't like grinding, if you're not very far, start over and put it on easy or very easy. You'll thank me later -- then you too can be level 30 and flying through the dungeons in the blink of an eye.
I recommend playing on easy. Its what I'm doing. Have never had to grind (but I still had to be tactful and fight the monsters I encountered).