Max Attack and Defense

To max the stats on a card you use the Arcana Forced ATK, Forced DEF, Forced ATK+ and Forced DEF+. The non + version increase the Attack or Defense stat by 50, while the + version increases the stat by 500. You can use one attack and on defense arcana at a time for a total of 2 arcana. These arcana can be applied either using fusion or Evolution & Amalgamation.

Since stats are only partially carried over during Evolution & Amalgamation, be sure to apply them only at the final stage of the card.

Maxing Stats cost effectively
Gold cost per arcana is calculated as   when using level 1 N cards as the material cards. For example, a level 6 card would cost  . If the card is at max level, the gold cost is doubled. For example, if upgrading a lvl70 GSR card, the formula becomes  . This means that upgrading a level 70 GSR card will cost more than upgrading a level 70 HUR or level 70 GUR card.

If you know you want to max the stats on a card, the worst option you can do is wait until it is max level.

Also remember that you can apply both the Attack and Defense arcana with a single material card.

Reducing Cost for cards available for Awakening
If you want to reduce Gold cost of increasing ATK and DEF of a card that can be awakened, you can apply some of the arcana before Awakening.

The best way way to save gold is to calculate the number of Arcana needed to max the GSR or GUR stats, then apply half while the card is still HSR or HUR (starting at level 1), and the other half after awakening (again starting at level 1).

For example, using our Chocolatier example above, the ATK at level 90 for a fully amalgamated version is 20904. So we calculate our needs as  . This tells us we will need 382 arcana to reach the max the higher stat (ATK) on our Chocolatier. We would then apply the first 191 to the HUR version starting at level 1. After awakening, the card resets back to level 1 again. Now we apply the remaining 191 arcana to the GUR starting at level 1.

Many cards, like Chocolatier, have different values for ATK and DEF. In these cases, calculate the upgrade count needed based on the lower stat. Start upgrading that, by itself, until the the difference is accounted for, then apply both together. The stats may still not be equal as the unawakened card may have a different stat spread than it's awakened version.