Gachi comes to reinforce your opinion of something or to highlight a critical situation and has gained popularity among Japanese teenagers. In particular, it replaced the colloquial word "maji" which means “in earnest” and “seriously”. “Gachi" is an abbreviation for the sumo term “gachinko(ガチンコ)". The meaning of “gachinko" means a “serious fight".
Ko, meaning child, refer to the noun. It's placement in the center of this compound word when composed with "Gachi" can mean either something earnest about a child/children in the abstract, or something earnest involving them, like something done to them, which is where the final term comes in
Ki here uses the Kanji for "tree" or colloquially "wood", but in actuality it's a reference to the erect male genitalia(literally, it's a relatively new term adopted directly from the English term "morning wood"). But since Japanese nouns like this can often shift between nouns and verbal nouns depending on context, and the sentence structure places this "Ki" at the end of the sentence(remember, Japanese sentences are SOV, so a sentence always ends on the verb!) means that the Ki used here is literally "to wood" - or, as you might've guessed it, to fuck
Putting it all together, since the subject of the sentence in Japanese is often left out due to it being a context heavy language, it's a shortened form of the sentence
Subject(The person referred to by the sentence) seriously children fucks, or to twist it into proper English, it means "A person who seriously has sex with children"