Dialogue in "Wild Dog: Splitter" is something that often needs to be done in the game, but dialogue often misses some things, so the thing you need to pay attention to in dialogue is to exhaust the dialogue. In general It means saying everything you can.
What should you pay attention to when talking to the Wild Dog Splitter
After completing a mission in Slitterhead, you will be taken to the "Conversation" tab of the game's main menu, allowing you to converse with rare items earned during the game. Doing so will not only lead to new quests and advance the story, but will also provide clues to more rare items.
Rare items, as playable characters in the game, will unlock more missions over time, giving you more things to do and different fighting styles to try. Be sure to exhaust all dialogue options in this tab before doing anything else, as this is a very critical part of the game.
If you want to re-listen to a previous conversation, you can go to the "Memories" tab in the menu, select the rare item you want, and select the conversation from the list of options. This is important because you may need to hear a prompt again to get a new rare item!