How's your 2025 was 2025 for you?

If you want to use wording closer to your original, it should be "How was your 2025?" or "How has your 2025 been?"

I went through so many hard times, emotional breakdowns, and distress, and I broke up.

"I went through many" was followed by two plural noun phrases ("hard times", "emotional breakdowns"), a singular noun ("distress"), and a verb phrase ("broke up"). Since you can't say "I went through many distress" or "I went through many broke up", I restructured the sentence.

However, despite the down sides, it' has also hadgiven me some great memories.

Your sentence would be fine in speech or informal writing. However, it's really you, not the year, that has the memories, so I changed the sentence accordingly.

These up and downs made me became a stronger person,. I'dve learnt how to embrace myself, and cherish the loves around me.

(1) You'd have to say "made me become" rather than "made me became". However, it's better to drop "become" altogether.
(2) You're talking about the year's effects on you now, so it's better to say "I've learnt" rather than "I'd learnt". (For what it's worth, as a US English speaker, I'd say "learned" rather than "learnt".)
(3) While it's possible to use the plural of "love", it's better to treat it like a mass/non-count noun here.

I hope 2026 can be a great year for both of you and me!

Happy nNew yYear!

How' was your 2025?

The past year, 2025, was not a great year for me.

I went through so many hard times, emotional breakdowns, distress, and broke eak-ups.

However, despite the down sides, it's also had some great memories.

These up and downs made me became a stronger person,. I'd learnted how to embrace myself, and cherish the loved ones around me.

I hope that 2026 can be a great year for both of you and me!

How' was your 2025?

"How's" can only contract "How is", not "How was"

I went through so many hard times, emotional breakdowns, distress, and brokea break up.

The rest of the items in the list are nouns, so it's more natural to also use the noun form of "a break up" rather than the verb of "broke up"

However, despite the down sides, it's also had some great memories.

These up and downs made me became a stronger person, I'dve learnt how to embrace myself, and cherish the loves(lives? things I love?) around me.

"I'd learnt how to embrace myself" - by putting it in the past tense, there's an implication that it's no longer true, like you've forgotten how to embrace yourself. As a result, it's better to use the present progressive tense to talk about your current state of having learned that.

"loves" - isn't clear what you mean here

I hope 2026 can be a great year for (both of you meand me / both you and me / both of us)!

Happy nNew yYear!

We typically capitalize wishes like this (for example, Happy Birthday!)

How' was your 2025?

I went through so many hard times, emotional breakdowns, distress, and I broke up with _____.

"to break up with someone" is a complete phrase, so if you say "and broke up" it isn't the same as saying, "I woke up."

Also, other things can "break up" such as a phone connection, or ice on a river or lake.

If you write "and a break up" many readers will probably understand what you mean, but then you have "break" twice in the same sentence.

The easiest solution would be to complete the sentence: "I broke up with my partner, my bandmates, etc."

However, despite the down sides, it's also had some great memories.

These ups and downs made me became a stronger person,; I'd learnt how to embrace myself, and cherish the loves----- around me.

It's not clear what "the loves" refers to. Everything you love? Everyone you love? Everyone who loves you?

I hope 2026 canwill be a great year for both of you and me!

We use "of" with the expressions, "both of us, both of them, both of you."
You could write "I hope 2026 will be a great year for both of us!"

We don't usually use "can" to talk about the future in this way. I'm not sure why we don't, but maybe it's because a year doesn't have the ability to make itself good?

I went through so many hard times, emotional breakdowns, distress, and broke a breakup.

However, despite the down sides, it's also had some great memories.

These up and downs made me becaome a stronger person, I'd learnted how to embrace myself, and cherish the lovespeople around me.

I hope 2026 can be a great year for both of you and me!