Those kids are terrible and I am no day at the beach either.
There is no definition on the internet, but it sounds like "I am trouble."
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"Day at the beach" is being used as a metaphor for something easy, enjoyable, and/or agreeable. Your guess that it means 'I am trouble' seems roughly correct: the speaker is suggesting that the kids are behaving terribly but that his behaviour is also difficult for those around him.
It's similar to the second (idiomatic) meaning of the phrase 'walk in the park'.
Since I can't comment (argh!)...
I would ammend to @jfhc answer and say it doesn't necessarily mean you're in trouble. It also can mean it's not as fun or easy. Whether it means trouble or boredom is a matter of context.
A day at the beach means swimming, sitting on the sand, eating hot-dogs and potato salad, maybe a beer.
If you're working a shift on the checkout-counter at McDonalds, it doesn't mean you're in trouble, just not having fun. After all, it's no day at the beach.
I would use this term to describe a situation or person that might be challenging.
It is preferred to use "isn't", but some people would use "ain't", which is non-standard[(1)] English.
- How’s your job?
- It ain’t no day at the beach. (It is tough, or I don’t like it).
- What’s it like working for your boss?
- He/she ain’t no day at the beach. (He/she is demanding/grouchy/difficult to get along with/incompetent)
- What was it like dating him/her?
- He/she ain’t no day at the beach.
- What’s it like looking for a job?
- It ain’t no day at the beach.