Making a point of trying horror movies with 〜ようにしている

Grammar Explanation: Making an effort to with 〜ようにする

Komura and Mie have spent the day at the aquarium. Now the two of them are walking together outside.

三重(みえ):: 「それでね」; “So, um...”; 「ホラー映画(えいが)苦手(にがて)なんだけど」; “I'm no good with horror movies, but...”; 「最近(さいきん)はちょっと観(み)てみるようにしてるの」; “...lately I've been making a point of trying to watch them a little.”
小村(こむら):: 「えっ…なんで？」; “Huh...? Why?”

Key Points

1観(み)てみるようにしてる, making a point of trying to watch

〜ようにしている describes something someone takes care to do as a regular practice. Mie isn’t talking about one movie. Lately, she has been making a habit of it.
ようにする puts effort behind the action. Horror isn’t something she’d watch for fun, so the watching takes a deliberate choice.
ちょっと keeps the effort modest: she watches a little, not whole marathons.

2観(み)てみる, trying to watch

〜てみる means doing something to see how it goes. With 観(み)てみる, Mie is testing herself by watching a bit, without promising to like it.
観(み)る is a spelling of みる used for watching films, shows, and performances. 見(み)る is the general spelling for seeing or looking.

3してるの, casual てる and soft の

してる is the casual contraction of している. The い drops out in speech.
The sentence-final の presents the statement as an explanation. It sounds soft and conversational, and it sets up her reason, which Komura asks for next.

4ホラー映画(えいが)苦手(にがて)なんだけど, setting up the background

苦手(にがて) means being bad at something or not liking it. Here it’s horror movies she can’t handle. The particle が after 映画(えいが) is dropped, as often happens in casual speech.
なんだけど gives background before the main point. な joins the な-adjective 苦手(にがて) to んだ, and けど leads into the contrasting news.
それでね picks the conversation back up. それで is “and so” or “then”, and ね keeps Komura’s attention.

ホラー (Horror): ホラー is the horror genre, stories in films, books, or games meant to frighten, often with ghosts or monsters. It usually comes before a noun, as in ホラー映画(えいが), “horror movie”.
映画 (Film): 映画(えいが) is a movie, a story told in moving pictures shown on a screen.
苦手 (Weak point): 苦手(にがて) means something one is bad at or someone one finds difficult to deal with.
ちょっと (A little): ちょっと describes a small amount or a short time. It also softens a refusal, or calls someone’s attention, like “hey”.
観る (To watch): 観(み)る is to watch something with attention, such as a movie, show, or game. It is a narrower spelling of 見(み)る.
みる (To see): みる is the kana spelling of 見(み)る, “to see”. After a て-form verb, it means to try doing something to see how it goes.
よう (Way): よう follows a word to show a way or manner, or that something seems a certain way. ようになる means to reach a point where something happens. It is also written 様(よう).
する (To do): する is to do or perform something. It also turns many nouns into verbs, as in 勉強する.
なんで (Why): なんで asks for the reason something happens. It is more casual than どうして.