I wish I have been there for the baby kicking for the first time?
Could I change the sentence to
I wish I was there for the baby kicking for the first time?
What are the differences between the two sentences?
Both sentences given are slightly incorrect, I’m afraid. I think the form you want is probably
(In speech or informal writing, this would often be contracted: “I wish I’d been there for…”) Also good, as Robusto said, is
although this only works if your absence was unintentional — if you knew when to expect it and just chose not to go, this version doesn’t apply.
are appropriate for an event happening right now, not for something that happened in the past. You might have a phone conversation: “The baby is kicking right now!” “Oh! I wish I were there for it!”
isn’t correct for anything (although it’s a fairly common error among non-native speakers, and people wouldn’t have difficulty understanding it).
If you weren't there, you should say
You're asking about the tenses, but notice that I changed the latter half of the sentence as well. To say "for the baby kicking for the first time" sounds kind of awkward.