This guide is been taken by other site....
-When you are speaking to the Alchemist, click on 'Upgrade' button to upgrade your item (all items with slots!!!) and then a new menu will appear.
This is a slotted item for example: 
-The Item space is to put the weapon or armor inside you want upgrading, the core space is to put your force core inside (you can also but low-, medium- or high core inside with the force core because it will increase the chance of being successful). The Catalyst space is where you have to put another slotted weapon / armor inside and this determines your special upgrade.
-You also can put a second force cores inside and can get a chance at getting a level 2 upgrade but its completely random what you get.
-When all is done you can click on the "try Upgrade" button. Now it can fail or success. I hope you get a success!
Upgrade List: 
Some Tips:
1.Only use low cores for increase the success rate!!! (thats important or you lose to much money)
2.The best lvl 1 Upgrades are hp and critic! (you can only make hp on suits and boots and critic on helm and weapon, for gloves much choose attack but you can also try lvl 2 upgrades)
3. First chance to get a success is 75% (if you have a double slotted item the second slot will have a 50% chance)
4. You also can increase the success chance with a catalyst which have +X (1,2,3,4,5...) which give 3% more.
Copyright by... http://shiningforce.ucoz.com/forum/15-10-1 .... (StrangeGorn)
Force Core Upgrade - Tips and Tricks - Written By StrangeGorn - Contributed By kr898
http://forums.playpark.net/showthread.php?t=305224
