The first
スリーピングエッグ・ゾーン
Sleeping Egg Zone
空に浮かぶ不思議な島。
A mysterious island that floats in the skies.
実はエッグマンが創りだした夢幻の世界なのだ!
But in reality, it's in fact a fantasy/dream world created by Eggman!
島のところどころにエッグマンの像があるのがいかにもアヤしい。
In the island there are Eggman statues in various places, it's really suspicious.
気をつけて、くれぐれも落ちないように・・・!
Be careful, be sure you don't fall...!
I think that the interesting keyword here is "夢幻の世界" (Mugen no sekai).
Fun fact, just by the sound, you could think of an "infinite world", but
the kanji here refers to something fantastical, illusory, or a dream. So anything in this context might be a valid translation of it.
Now for the second one
アクアプラネット・ゾーン
Aqua Planet Zone
異次元世界の水惑星・・・
A water planet from a different-dimensional world...
奇妙な生きものがウヨウヨしている。
Strange creatures swarm.
水の中に入ったら息つぎを忘れずに。
When entering the water, don't forget to take a breath.
The interesting keyword might just be the first part "異次元世界の水惑星"
水惑星 is literally "Water Planet"
異次元世界 is literally Different Dimensional World.