What is the best Special Offering?

The pick changes when you go in alone. Solo runs want Primary Attacker instead.

The offering is chosen by the team before a Holo Battle Interlink boss fight, and it is a battle buff that modifies the whole fight. Crushing Momentum is the safe default because it holds up when you cannot plan around your teammates. In a random matchmade group you do not know who will bring damage, break, healing or support, and Crushing Momentum is still the right call there. It also stays the recommendation as the season goes on, so you do not need to switch to something else once your team gets stronger.

Crucial Momentum is a different offering with a very similar name, and it is easy to grab by mistake. It works against the main boss, but it is not the top pick. Check that you have Crushing Momentum selected before the fight starts.

For solo play, including solo Alpha Luminel runs where you want as much damage as possible, Primary Attacker is the better buff. Crushing Momentum is the group answer.