sed：最初に出ていない行と前の行を削除します。

これを行うには、awkを使用します。

$ cat tst.awk
(!NF) {                # blank line
    b = ""; f = 1      # empty buffer, start buffering
}
/-->/ {                # timestamp
    f = 0              # stop buffering
    if (p == $0) {     # same timestamp
        next           # discard buffer, start over
    }
    p = $0             # save timestamp
    printf "%s", b     # print buffer
}
f {                    # buffering enabled
    b = (b $0 ORS)     # buffer line
    next               # start over
}
1                      # print line

出力：

$ awk -f tst.awk file
231
00:13:35,230 --> 00:13:37,120
- Oh, my sister got me into it.

232
00:13:37,129 --> 00:13:38,269
- Yeah?
Is that her?

234
00:13:40,049 --> 00:13:41,090
- Yeah.