Case is related with Milestones through Entitlement. So, you can show the Entitlement Record on Case level, but Milestones records cannot be displayed at Case level at least through formula fields.
You can create custom fields at Case and from apex coding populate those values from Milestones. But a Case can have multiple milestones. So you need to think which milestone record to be shown on Case level.
Update based on comments
When the milestone is violated you can define workflow field update action to update a Case field.
To define this:
Go to Entitlement Process --> Milestone --> Violation Action
Add time trigger: 1 Minute After