CATALYST
The catalyst is to determine which stat your equipment you're upgrading will have. And your catalyst must be slotted so don't be surprised if you cannot place a non slotted equipment inside.
An upgraded (eg. +1/2/3/4...) catalyst will further increase the success chance. See the difference in success chance as compared to the first screenshot? (my catalyst is a +5 in my case)
Refer to the picture below to see what catalyst gives what stat :
Things to take note of:
1) Some equipment are unable to receive a certain stat (
eg. in the first column, only boots and suits are able to achieve a HP stat)
2) Just in case people forget, level 2 upgrades are random and cannot be determined by the use of catalysts. But to play safe, always make sure what level 1 upgrade you want if the level 2 upgrade fails. (
reason being if you didn't make to a level 2 upgrade, at least the next option will be the desired stat you want thanks to the catalyst instead of a random level 1 upgrade stat)
3) The catalyst used must either be one grade less/equal or many grades higher than the equipment you're upgrading (
eg. for Osmium, as a catalyst the lowest grade usable is Shadow Titanium. Anything Osmium or higher is usable)
4) If you fail an upgrade, only the catalyst and force core (or upgrade cores) used will be gone. The equip you're upgrading still remains.
5) Regarding the upgrade stats list, there are "mistakes" pointed out by a lot of people. The only reason i can think of is that this is not an updated list but for what stats you can achieve remains correct.