Inherit skills

Those are skills that comes with the demon after a fusion, the demon may or may not have it fully unlocked after a fusion. I'll try telling how you can train those skills.

For your demon to make use of that skill, you need to have it fully trained and placed on the skill slot. If you fuse that demon without learning that skill, It will be lost for good.

Fire
Make your demon be hit by any skill of Fire attribute.

Ice
Make your demon be hit by any Ice attrbute skill.

Electric
Make your demon be hit by any Lightning attribute skill.

Force
Make your demon be hit by any Force type skill.

Rush
Make your demon be affected by any Rush Action Type skill.

Curative
Curative Skills are unlocked either by using Curative affinity Skill or Items on your demon.

Unless you have a party member to use curative spells on your demon, or your character have curative spells to use in your demon, you may try going to the Pharmacy and buying a stack of Dis- Items from the store, then keep spamming it near the demon until the skill unlocks.

Support
Support skills are unlocked by either using Support Affinity skills or items, be it benefitial or prejudicial buffs.

You may try making demons cast debuffs on your demon, but that will take way too long to train. Or a party member use buffs on your demon, or even you, if you have unlocked a buff spell.

The other solution is going to a Magic Shop and buying several Rakukaja Stones, then repeatedly use it on your demon.

Defensive/Passive
Those are trained the same way, either make your demon attack another demon or player that is with a defensive skill active, or keep spamming defensive skills on your demon while another demon or player tries to attack it.

Those skills may be Guard type, Counter Attack or Dodge.
 * Rainbow of Victory Jack Frost -> Keep using Counter attack.
 * Kissy Pixie -> Keep using Dodge skill.

Expel
Have your demon be affected by Expel affinity skill.

Death
Have your demon be affected by Death affinity skill.

Mind
Have your demon be affected by Mind affinity skills.

Mystic
Have your demon be affected by Mystic affinity skills.

Long Range
Have your demon be affected by Long Range affinity skills.

Penetrate
Have your demon be affected by that kind of affinity skill.

Almighty
Have your demon be affected by Almighty affinity skill.

Most likelly bosses have this, so you may want to have your demon well leveled up before trying to train it.

Nerve
Nerve affinity skills increases this, but Mind type skills also helps the demon learn this kind of skill, but a bit slower.