I saw the BCM/CM tip here before but its not clear whether it can be used with the FX-888 as it doesn't show it as a replacement tip in the manual - also can't find anywhere that sells them. Having endured the necessity of struggling with whatever crappy tools were available in my former employment at sea, I now have the luxury of being able to choose my own tools and would prefer to use the best tool for the job so other methods suggested would not be my first choice.
The FX-888 can take any T18 style tip and also the older 900M style tips. So when buying tips that's all you have to check.
As mentioned above the cup ended tips have legal blockages on them, so you would probably have to import them directly from Japan or something.
But honestly, if you have only ever used a crappy iron the FX-888 will be a revelation. It is a really good iron whatever tips you use with it. If you get one you will invent reasons to do soldering just so you can smile.
My favorite trick with the FX-888 is touching the tip to the outside of a big lump of metal like a banana plug and heating the whole thing up to soldering temperature. The iron just pours heat into it until the solder melts.
The cup shaped tips are probably nice, but it's no disaster if you can't get hold of them. With soldering as with anything, a job is made or broken by the skill of the practitioner. A good practitioner can succeed even with limited tools, but a poor practitioner will produce poor results with any tools good or bad.