Finding words with specific criteria in a text in python
You don't need anything sophisticated to do this. It can be achieved with simple string matching, with a few caveats:

Animals - simply create a list of animals you want to recognise. You can probably find lists of animals on the web, Wikipedia, or similar. The complication is that you might need to trim a plural marker (horse/horses — I'm assuming English here). You could simply look up each word in the list, and if it's not in there and ends in -s, look again with the final s trimmed off. Irregular plurals exist (ox/oxen), but there are very few of those.
Superlatives - again you can create a list. Superlative forms usually end in -est, so just get an English word list, throw away everything that doesn't end in -est, and then go through the remaining words removing false positives like nest etc. There will also be some irregular ones. How do you want to treat combined ones, such as most beautiful? In that case you might check for most followed by an adjective.

For superlatives there would be a second, more complicated, option, and that is using a part-of-speech tagger. Tag your text, and then get all words that have been tagged as superlative adjective. In most English tagsets that will be JJS. But taggers are not necessarily better than a word-list in terms of accuracy, so it depends on how much effort you want to spend on it.
You gave those as examples. For many other categories of words there are similar ways of just extracting them fairly easily, without needing complicated machine learning systems. But don't forget that creating lists might be a low-tech solution that might be quickest and most easy, with the best accuracy.
I have a text and want to find e.g.

All Animals
All Superlatives

Is there a "simple" way to do this?
Im completely new to NLP.
Im not even sure if this is a NLP Problem in the first place.
Or does this just sound simple and is actually very complex?
If you have a tip for adding/removing tags on this question all feedback is welcome.