Can someone explain the lore to me?

[Αη Ιnτellecτual Tsiραr]

who is diein and the tattoo guy. I am curious as to the plot but I can't find much on the internet about it so I am asking the steam community. Thank you

[Shadic]

You can find info on each song on Namu Wiki[en.namu.wiki] which is a korean wiki.
For example Glory Day[en.namu.wiki].

There's a story order to play the songs in also (taken from reddit):
01 Forte Escape - Ask to Wind ~Live Mix~ (P1)
02 Ruby Tuesday - Your Own Miracle (P2) [these two songs introduce DJMAX and the protagonist]
03 M2U - Nightmare (P2)
04 TAG - Vertical Eclipse (EXT4) [these are the events before Respect]
05 BEXTER x Mycin T - Glory Day (Respect)
06 BEXTER - BlackCat (Respect)
07 BEXTER - Boom! (Respect V)
08 BEXTER - Dream it (EXT2)
09 Raven & Kreyn - So Happy (Respect V)
10 SSOMbo - Over Me (EXT2) [these two are side stories]
11 ESTi - U-NIVUS (Estimate)
12 Mycin T x SiNA - Daydream (EXT2)
13 TAK x Corbin - Tic! Tac! Toe! (EXT3) [this part introduces Lena from Tapsonic]
14 ND Lee - LUV (EXT4)
15 TAK x Sobrem - DIE IN (EXT4)
16 TAK - Glory MAX -to the MAXimum- (EXT5)
17 Sampling Masters AYA - Revenger (EXT5)
18 Pure 100% - Peace Comes at a Price (EXT5)
19 Pure 100% - Final Hour (Game Ver.) (VLIBERTY)

Diein and Gaya (the tattoo guy) are introduced in Nightmare/Vertical Eclipse.
The story isn't directly told so I would watch the BGAs and read the descriptions for each song on Namu Wiki and also this reddit thread is very helpful.

For side characters this list helps too.

[Αη Ιnτellecτual Tsiραr]

Thanks for the very detailed and helpful answer. I remember finding a djmax wiki but it hadn't been updated in a long while so this is all very helpful. Thank you again