Trying to model a process on process in DV 2.0.
If a payment contains 1-1 mapping with transfer and each transfer contains 1-many mapping with attempts, how should I model my data vault
Unable to understand how to model these scenarios of one process initiating another processes in Data Vault 2.0

First of all, link are designed to be a many-to-many relationship only. this cover all relation that could exists in past, present and future (if business logics change, you won't have to redesign your DV).
Second, do not create a link-to-link relationship, that is bad design. A link must represent relationship between business entities, not between business entities and relationship.
To answer your question, take a look at the transactional link (aka non-historized link), it should suit your need. without having your model, here's what the transaction link could look like :