All things means all things in the sense of each and every part that applies. The context shows us what things are meant. So the all things is this verse is hoping.
The Greek word translated “hope” is from elpidzo, meaning “to hope or wait for salvation with joy and full confidence.” This word expresses more than a wish or desire, but a confident belief in the unseen.
Biblical hope is different from human hope. We hope is won't rain and spoil our picnic or we hope our team wins the game. This is not the kind of hope talked about here. The hope here is grounded the Word of God and because we know that God cannot lie, our hope is solid, full of confidence and joyful anticipation. "Now faith is the reality of what is hoped for, the proof of what is not seen."( Hebrews 11:1) Most of the hope the New Testament talked about was the hope in eternal life with Jesus. When we have this kind of hope, we live our life from a different point of view, an eternal one. But "hope all things" is not just believing that after we die everything will be better. It is grabbing a hold of God's promises for us now.
Agape grounded hope is actively waiting for God's fulfillment of what God has promised. Abraham is used as an example of this hope. God promised him a son, but at 99 years old, the promised son had not been born. Romans 4:18 says . "Against all hope, Abraham in hope believed". This hope is not something we work up by our self, it comes as a gift from God through grace. "Now may the God of hope fill you with all joy and peace in believing, that you may abound in hope by the power of the Holy Spirit."(Romans 15:13)
As we receive this gift, he will tell us any steps we are to take for those thing hoped for to come to pass. That is the actively waiting part. Abraham and Sarah had to take an active part is bringing their promised son to birth. We are not to sit idle and wish real hard, but to " wait in silence for God only, For my hope is from Him."(Psalm 62:5 ) He will give us the wisdom to get the active part right.
" Know that wisdom is thus for your soul; If you find it then there will be a future, And your hope will not be cut off. Without God’s wisdom which gives God’s hope, your hope will be in the wrong thing and it will be cut off."Proverbs 24:14
What are the "all things" you hoping for? Find your promise in the Word of God, get His wisdom, obey what you hear him tell you to do. Then wait for it happen with full confidence and joyful expatiation. Now you are hoping the agape way!