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Pchh can be obtained in tpoint shop rare chance though
Dp shop (PL near grocer. I tried once)
Key of chaos lvl 6 legendary box (0.0035% chance not sure)
Sghh/sgh can be bought at ecoin shop and ecoin is farmable now
SGH/SGHH are obtained through tpoints as well. 1-50 (RNG).
Perfect Cores are obtained through extracting items +13/+14/+15. The core depends on the grade of the corresponding item.
There is a low chance in Chaos Arena Lv. 6, ofc. Ryayyy almost answered your questions completely.
Make sure to do the Daily Activeness Tasks in order to obtain E-Coins.
All upgradables are also obtained through Itemshop/NPC in exchange for E-coins & V-coins.