Your sample data doesn't have this format "%m/%d/%Y %H:%M:%S", apparently those are difftime values, not POSIXct values, so you should use hms() function instead.
df <- data.frame(Category = c(1L, 1L, 3L, 2L, 2L, 1L, 3L, 1L, 3L),
Date_Time = c("55:15.0", "26:58.0", "42:18.0", "26:58.0",
"55:15.0", "49:57.0", "36:59.0", "53:34.0",
"10:48.0"))
df %>%
mutate(Date_Time = hms(Date_Time))
#> Category Date_Time
#> 1 1 55H 15M 0S
#> 2 1 26H 58M 0S
#> 3 3 42H 18M 0S
#> 4 2 26H 58M 0S
#> 5 2 55H 15M 0S
#> 6 1 49H 57M 0S
#> 7 3 36H 59M 0S
#> 8 1 53H 34M 0S
#> 9 3 10H 48M 0S