めったに〜ない details

hardly ever + write + not

metta ni kakanai

hardly ever; rarely — the occasions are so few that one of them is worth remarking on

meaning: hardly ever write

私わたしは、朝あさのニュースをめったに見みない。

watashi wa, asa no nyuusu o metta ni minai.

I hardly ever watch the morning news. neutral

あいつがあんなに褒ほめるなんて、めったにないことだよ。

aitsu ga annani homeru nante, metta ni nai koto da yo.

For that guy to praise it that much — it hardly ever happens. casual

Examples

hardly ever; rarely — the act happens so seldom that the speaker treats each time as an exception

私わたしは、朝あさのニュースをめったに見みない。

watashi wa, asa no nyuusu o mettaniminai.

I hardly ever watch the morning news. neutral

あいつがあんなに褒ほめるなんて、めったにないことだよ。

aitsu ga annani homeru nante, metta ni nai koto da yo.

For that guy to praise it that much — it hardly ever happens. casual

この駅えきに特急とっきゅうはめったに止とまりません。

kono eki ni tokkyuu wa metta ni tomarimasen.

Express trains hardly ever stop at this station. neutral

これほどの品しなには、めったにお目めにかかれません。

kore hodo no shina ni wa, metta ni ome ni kakaremasen.

An item of this quality is one you rarely get to see. formal

滅多に — the kanji spelling; kana is commoner in print, and neither shape releases the adverb from needing a negative.
めったにない — hardened into a modifier meaning "rare" — めったにない機会きかい, where the negative belongs to the phrase rather than to a following predicate.

めったに counts occasions, so it wants a repeatable event — a one-off has no
frequency to be low.

あまり〜ない
Two different scales — あまり cuts the DEGREE of one act (あまり食たべない leaves food on the plate), めったに counts the OCCASIONS (めったに食たべない says the plate is almost never in front of you).
時々
Neighbours on the frequency scale, either side of the reportable line — 時々 grants that the occasions do happen and treats them as unremarkable, めったに〜ない denies nearly all of them while leaving the rare exception standing.

よくplain-antonym
Same pre-verbal slot and the same job of counting occasions, at opposite ends — よく claims the act is the norm, めったに〜ない puts it near zero, and unlike よく it is ungrammatical without the negative (×めったに行いく).

ろくに〜ない
Both are adverbs that hang unfinished until a distant ない, but ろくに attacks the QUALITY of an act that did happen (ろくに読よまないで返事へんじした — read it badly), while めったに says the act nearly never happens at all.