FDB's answer seems accurate: it's not actually a Latin word for "nightmare", but has been mistakenly believed to be one.
Where does "tantibus" = "nightmare" orginally come from? It seems attested no earlier than 2000
On the USGS website, I found an artistic image of elevation data from the Shuttle Radar Topography Mission that was released by the Earth Resources Observation and Science Center. It is titled "Tantibus" and appears with a note "Tantibus is Latin for nightmare." This appears to have been distributed as part of the "Earth As Art" series (e.g. in the Earth as Art 5 collection, November 2018). The webpage has an earlier date, but I'm not sure exactly what that means (see the following section).
I'm not sure this is really from 2000; its origins are mysterious
The web page gives the date of January 31, 2000. It's not clear what this is supposed to mean (the date of the photography the image is based on, or the final image itself?), and I'm not sure how to verify that it is the correct date of either of those things. There is some reason to suspect that the image might actually have been created at a later date: according to Wikipedia, "The SRTM was flown on an 11-day mission of the Space Shuttle Endeavour in February 2000"; so if the image is in fact from the Shuttle Radar Topography Mission, it seems impossible for an image from that mission to have been posted online on January 31, 2000. I noticed Google search also shows January 31, 2000 as the date of the web page, but unfortuately, it seems that Google doesn't have a single procedure for determining which date to display for search results, so it doesn't tell us anything much since Google might be just copying that directly from the text on the present-day webpage. The oldest copy on the Internet Archive is only from 2020. This does provide the useful information that January 31, 2000 was previously listed in a "Date Taken" field.
The image is public domain, probably as a government creative work; I haven't found any attribution of the artist who selected the image, gave it this title or wrote the description.
If the date isn't too far off, this would be the earliest example I've found so far, and I'd guess it was the direct or indirect inspiration of all subsequent examples. If the date is just (approximately) for the photography, I have no clue where it fits in relative to the following examples, and there's a possibility that the author of the title and caption as well as others got "tantibus" from a statistical machine translation service like the old version of Google Translate.
Other examples through the years
I initially thought this mistake originated in the name of the nightmare-themed My Little Pony: Friendship Is Magic character Tantabus that you mentioned (appearing in Season 5, Episode 13 "Do Princesses Dream of Magic Sheep?", July 11, 2015). However, after I did a bit of digging on the edit history of wiki articles for the My Little Pony character and other possible examples of "tantibus", I found the following examples from before the introduction of the MLP character:
The relevant MLP wiki edits are as follows:
The text "Tantabus is Latin for the word 'nightmare'." was inserted on the Villains Wiki article "Tantabus" on 29 July 2015.
This was edited on 3 October 2015 to read "Tantibus (Alternate spelling for Tantabus) is Latin for the word 'nightmare'.", with the edit comment ""Tantabus" is not a latin word, "Tantibus" is."
The text "The name "Tantabus" is a corruption of "tantibus", a Latin word for "nightmare."" was inserted on the My Little Pony Friendship is Magic Wiki article "Creatures" on 18 March 2016. Therefore, the timeline is consistent with this article being based on the Villains Wiki article.
At some point, it made it into Google Translate in some fashion
Currently, Google Translate does not suggest "tantibus" if you enter "nightmare" in the English-to-Latin direction.
However, if you enter "tantibus" in the Latin-to-English direction, it does translate it as "nightmare". So in some manner, Google Translate sees a connection between "tantibus" in Latin, and "nightmare" in English.
Unfortunately, I don't know the technical details of how Google created Google Translate for Latin. However, it seems possible that at some earlier point, it offered "tantibus" as a translation in the English-to-Latin direction for "nightmare". Many people trust Google Translate when they shouldn't; that would help explain some of the spread of the belief that "tantibus" means "nightmare" in Latin. However, this is just a hypothetical scenario; I'm not certain that Google Translate ever did this.
According to Wikipedia, Google Translate was only launched in 2006, and Latin was only added in September 2010, so if Google Translate was the source of this error, the final image shown on the USGS website must have been created more than ten years past the date when the original source image was taken.