Translation:I sometimes go to the sea by myself.
IME, 海[うみ] is what Japanese people usually say if they're going to the beach (as opposed to 浜[はま]). Of course it could mean they're going to a non-beach seaside location, but hearing this sentence without further context my immediate assumption is that the person is going to the beach.
Yes, very clever, but scale does matter: The smaller a land mass and the greater the deviation from a circular shape, the higher the ratio of coastline to area and the shorter the average distance to the coast. So, even though not all coastline might be considered beach, yes, Japan does have beaches. Try Googling something like beaches near Tokyo, etc.
When your dog dies, your hat business fails, grandpa and grandma pass away and you break up with your girlfriend.. there is no choice but to go the sea alone
You can, but "sometimes" is a more natural translation that better encompasses how you would use it in Japanese.
"Go into" by itself would be 「～の中に行く」（中＝なか）, but that sounds unnatural in Japanese (it literally translates as "go to the inside of ~"). The natural way would be to actually use the verb 「入る」（はいる）, "to enter", like so:
「ときどき一人でうみに入ります。」, with full Kanji: 「時々一人で海に入ります。」
I wrote ときどき一人で海に行きます and was marked wrong because I wrote umi in kanji rather than hiragana. :(
I couldn't report that this was the problem either. :'( 07/25/18
Considering the other listening exercises have struck me down for my usage of kanji, i entered everything in kana (not unreasonable for listening exercises, IMO), and got told to use kanji. Not being able to report this is indeed vexing.
ときどき一人で海に行きます。Marked wrong. Come on, Duo. Kanji are part of the Japanese language and you should accept them in answers.
Report it. Japanese is a newer language on Duo and still has some kinks in it.
「自分で」usually implies doing something by yourself in the sense of "without assistance". For example you could say something like 「自分でご飯を作ります」(I cook for myself). Saying 「時々自分で海に行きます」 would only make sense if you ordinarily go there with help (i.e., someone drove you there), for example: 「だいたい友達が運転してくれますが、時々自分で海に行きます。」
"I go to the sea by myself sometimes" wasn't accepted. Is it not correct?
Memorize it. If that is hard, use a memory aid like "He told Lee that he's alone." He told Lee sounds like ひとり and may help you remember it means alone. 一人 (ひとり) is a common word in Japanese. If you read stories in Japanese and listen to songs you will probably learn it by repeated exposure to it.