Does a Seeker of the Way affected by Arcbond deal one batch, or multiple sets, of damage?
I would say that Ajani's Pridemate only gets 1 counter.  


  702.15b Damage dealt by a source with lifelink causes that source’s controller, or its owner if it has no controller, to gain that much life (in addition to any other results that damage causes)


And for damage:


  119.4. Damage is processed in a three-part sequence.
  
  
    119.4a First, damage is dealt, as modified by replacement and prevention effects that interact with damage. (See rule 614, “Replacement Effects,” and rule 615, “Prevention Effects.”) Abilities that trigger when damage is dealt trigger now and wait to be put on the stack.
    
    119.4b Next, damage that’s been dealt is processed into its results, as modified by replacement effects that interact with those results (such as life loss or counters).
    
    119.4c Finally, the damage event occurs
  


In this case, there is a single source, and a single event of damage.  Yes, it's hitting multiple things, but it's only one event of damage. 

Additionally, Gatherer says of Ajani's Pridemate:


  A creature with lifelink dealing combat damage is a single life-gaining event. For example, if two creatures you control with lifelink deal combat damage at the same time, Ajani’s Pridemate’s ability will trigger twice. However, if a single creature you control with lifelink deals combat damage to multiple creatures, players, and/or planeswalkers at the same time (perhaps because it has trample or was blocked by more than one creature), the ability will trigger only once.