What is the Catholic interpretation of Soteriology in the Bread of Life Discourse in John chapter 6? Catholics interpret the Bread of Life Discourse in John chapter 6 in light of transubstantiation (= the miracle of bread changing into Jesus' literal flesh and wine changing into Jesus' literal blood performed by a Catholic priest in the person of Jesus Christ.Only the substances changed into Jesus's substance and not the appearances of the bread and wine). (source)

In the Bread of Life Discourse in John chapter 6, Jesus said [in light of Catholic Dogma of Transubstantiation]:

John 6:35 Belief in Jesus = eternal life

John 6:36 Belief in Jesus = eternal life

John 6:40 Belief in Jesus = eternal life

John 6:47 Belief in Jesus = eternal life

John 6:64 Belief in Jesus = eternal life

John 6:54 [literally] eat the flesh and drink the blood of Jesus = eternal life

John 6:55 [literally] eat the flesh and drink the blood of Jesus = eternal life

John 6:59 [literally]eat the flesh and drink the blood of Jesus = eternal life

Was Jesus teaching about TWO WAYS to have eternal life in the Bread of life Discourse in John chapter 6? 

1) Belief in Him

2) Eat his flesh and drink his blood

What is the Catholic interpretation of Soteriology in the Bread of Life Discourse in John chapter 6?
Jesus didn't teach just one or two things necessary for salvation. Cf.


  And he said to them, “Go into all the world and preach the gospel to
  the whole creation. He who believes and is baptized will be saved;
  but he who does not believe will be condemned. - Mk 16:15-16.


And


  Go therefore and make disciples of all nations, baptizing them in the
  name of the Father and of the Son and of the Holy Spirit, teaching
  them to observe all that I have commanded you; and lo, I am with you
  always, to the close of the age.” - Mt 28:19-20


From these two passages one can readily see that baptism and observing ALL the LORD commanded the disciples are necessary for salvation.

And the Church teaches that we are to receive the LORD in the Eucharist or else we will have no life in us:


  CCC 1384 The Lord addresses an invitation to us, urging us to
  receive him in the sacrament of the Eucharist: "Truly, I say to you,
  unless you eat the flesh of the Son of man and drink his blood, you
  have no life in you." (Jn 6:53).


Based on the Bread of Life Discourse in John chapter 6 this is the Church's teaching on the necessity of receiving the Eucharist for our salavation.