RPG Insanity

There are 11 "special drops" only available from boss monsters:
1.Dark Knife
2.Intuition Hood
3. Spirit Crown
4. Valkyrie Lance
5. Phoenix Suit
6. Slumber Sword
7. Spirit Robe
8. Reflect Stick
9. Sunrise Plate
10. Firedrake Helmet
11. Spirit Shield
The order matters, as the first special drop will always be the Dark Knife, and the last will always be the Spirit Shield.

It is possible that all of the boss monsters may have a special drop, but I tested only those NOT in the bonus material, and not even every boss. The drops are random: they do not always occur, and any boss may drop any of these items. The same boss can drop more than just one item (but of course only one per battle). Unfortunately, every boss has a "timeout" when it will refuse to engage in a battle (it will say something like, "Come back tomorrow"). I do not know for certain how long this timeout period is, as it could be a few realtime hours or even the next calendar day.

It is possible that only one "special drop" is available per timeout period. I cannot prove that, but that is what happened to me. The Japanese Wiki (via Google translate) states "strong boss (resurrection when crossing dates in real time)."  Perhaps I got discouraged when I defeated several bosses and didn't get any drop and waited until the next day to try again.  The Japanese Wiki seems to indicate that each  special drop only occurs after a number of victories, perhaps as many as 10,  over these "strong" (special bosses).

ADDED NOTE:

Thanks to intense study by @Mastertrek, it appears that the interval between "special drops" is based on raising the combined level by a total of 10 for the special bosses.  That is, you can raise a single boss 10 levels, or 2 bosses 5 levels each, or any combination of bosses that totals 10.  The back and forth postings in this topic show us trying to figure out exactly what it takes to get a "special drop," and I believe that Mastertrek's proposed solution is correct.

The bosses in the following locations all seemed to be part of the special drop feature: E Tower, West Cave, Port City, Elven Village, Forest Castle, Empire, Light and Dark Cave, Wind Tower, and Desert Castle.
[Note: I did not try the bosses in the Volcano of Essence.  The Japanese Wiki states the special drops all occur from bosses in the 9 locations listed above.]
I did not test other bosses, and although the Dragonlord can perhaps (not sure) drop special items, I suggest you avoid its battles so that you can obtain all the drops prior to completing the game (that is, prior to using clear data for bonus material). You will need to obtain all these special drop items if you wish to complete the "Item complete" listing in the "Record" menu item.

Kudos for getting all 11 items! I think I got two of them before I got frustrated and gave up. 

I have to say, for a game that has no real story and absolutely no clues on what to do or where to go, this one turned out to be one of my favorite JRPGs ever (well, on mobile, anyway).

Maybe you found out how to get these items to appear because I tried boss in E. Tower around 50 times with no drops yet (I kept resetting at boss level 10 each time I got there.)

You need to understand how these drops work.  For each drop, there is only ONE monster that will yield the drop (and it is a random boss monster).  So if you try monster x a few times and don't get a drop, move on to a different boss monster (choose from the list of locations I mention in my post).  Once you get the drop, you will have to wait for the "time out" to get the next drop on the list.  Once again, it will be only ONE random boss monster that gives you the special drop.  So trying the same boss over and over (as you mention in your post) will not be successful.

Oh, ok. Thanks For now I have every boss unlocked except Empire, Light and Dark Cave (don't know how to go through the area but all the info says that different stairs show up for different elements. Maybe it's about who is the leader.) and Dragonlord Castle (visited all areas I have access to via ship).

Also I have 8 people total in party now. I'm sure I'll get somehow the elven village person and I have to grind for Claw if I'm right. 

And another question : Can I get the drop again from boss or all of the items are one time only?

And do I keep everything at ng+? Edit : never mind about that question). 

And The Time out requires to wait for the next day to start for the bosses to accept challenge again.

Each special item only drops once, no repeats.  The boss may drop a different special item, but the bosses are chosen randomly, so you just have to try them one at a time until you get the drop, then wait for time out, and then go after the next drop on the list.  Yes,  you keep the items for the ng+.

So that means even at ng+ the bosses won't give them again?

Current stats (some)