1. At the pro-wrestling match, the wrestler beat his opponent with his heading.

2. At the pro-wrestling match, the wrestler defeated his opponent with his heading.

3. At the pro-wrestling match, the wrestler beat his opponent with his headbutting.

4. At the pro-wrestling match, the wrestler headbutted his opponent in the ring.
[Which ones are grammatical? Do you have better expressions?]

Instead of "heading," you should use use "headgear."

https://www.google.com/search?q=wrestling+headgear&source=lnms&tbm=isch&sa=X&ved=0ahUKEwi039SE6InZAhXBq1kKHQsjAM0Q_AUICygC&biw=1437&bih=716

If you make that change, 1 and 2 are correct.

In 3 and 4, the word should be spelled "head-butt" (with the hyphen): https://dictionary.cambridge.org/us/dictionary/english/head-butt

I'd re-write them a bit --

3. At the pro-wrestling match, the wrestler beat his opponent by head-butting.

4. At the pro-wrestling match, the wrestler head-butted his opponent in the ring.

Out of the four sentences provided, 2 and 4 are grammatically correct. Here's an explanation of why:

1. "At the pro-wrestling match, the wrestler beat his opponent with his heading."
This sentence is not grammatically correct because "heading" is not typically used in the context of pro-wrestling to refer to a move or technique.

2. "At the pro-wrestling match, the wrestler defeated his opponent with his heading."
This sentence is grammatically correct and conveys the idea that the wrestler won the match using a move or technique involving his head.

3. "At the pro-wrestling match, the wrestler beat his opponent with his headbutting."
This sentence is not grammatically correct because "headbutting" is a gerund form (verb used as a noun) and does not fit well in this sentence structure. It would be better to use "headbutt" as a verb instead.

4. "At the pro-wrestling match, the wrestler headbutted his opponent in the ring."
This sentence is grammatically correct and effectively communicates that the wrestler used a headbutt move on his opponent during the match.

Alternative expressions could include:
- "At the pro-wrestling match, the wrestler defeated his opponent with a powerful headbutt move."
- "During the pro-wrestling match, the wrestler emerged victorious by executing a devastating headbutt on his opponent in the ring."