If I have two tackle icons on a card, I can tackle twice in a turn, yes? Can I thus tackle a player and, if successful, attempt to injure him?
Likewise if I play an upgrade that gives me a tackle icon, I assume that can give me a second tackle icon if I already have one.
Yes to both.
The only caution is that some cards allow you to target different players each time. So you can only tackle each player once and cannot use additional tackles to injure them.