I don't think that you can go far wrong by following guidelines like this one, which states:
Rule 1. Generally, hyphenate two or more words when they come before a noun they modify and act as a single idea. This is called a compound adjective.
In your sentence, the words "Spring", "Boot" and "based" form a compound adjective that modifies the noun "approach".
But wait: "Spring" and "Boot" are proper nouns. Reading down a little further, you come to this rule:
Rule 9a. Do not hyphenate proper nouns of more than one word when they are used as compound adjectives
It doesn't say what to do if only two of the three words are proper nouns. Looking at actual usages you will find that the proper nouns are not hyphenated, but other nouns are. Here are a couple of examples:
In Stone Building, Kevin Gardner distills his decades of experience building and maintaining iconic New England-style stone walls into this concise, informative guide - Stone Building, Kevin Gardner 2017
This chapter investigates these issues via a case study of a West London-based record company - Western Music and its others, Georgina Born and David Hesmondhalgh 2000
These examples seem to fit with rule 1 modified by rule 9a, which suggests that the correct way of hyphenating your compound adjective would be:
a Spring Boot-based approach
That said, punctuation is not an exact science, especially when dealing with obscure points like proper nouns. A fully-hyphenated version is unlikely to ruffle too many feathers:
a Spring-Boot-based approach