For green Irelia champion, if I play a spell and target her to get a +1, if my opponent counters the spell, do I still get the +1?

Yes, you still get the +1 Might bonus.

According to RiftJudge FAQ #9108 and #9163, this interaction works because of the timing of when "choosing" occurs and how the chain resolves:

Why Irelia still gets the bonus:

1. Trigger Timing: Irelia’s triggered ability ("When you choose... me") triggers at the moment she is chosen during the spell's finalization process, which happens before the spell is fully on the chain and before your opponent has an opportunity to play a "Counter" effect.
2. Independence on the Chain: Once the trigger condition is met, the triggered ability is placed on the chain as a separate item, sitting above the spell that targeted her.
3. Resolution (LIFO): Even if your opponent counters the spell, the spell is removed from the chain and goes to the trash, but Irelia’s triggered ability remains on the chain. Because the chain resolves in LIFO (Last-In, First-Out) order, her ability resolves normally, granting her the +1 Might.

Sequence of Events:

1. Play: You play a spell and choose Irelia, Fervent as the target.
2. Trigger: Irelia's ability triggers and is placed on the chain on top of your spell.
3. Counter (Reaction): Your opponent plays a "Counter" effect targeting your spell.
4. Resolution:
   • Irelia's triggered ability resolves first: She gains +1 Might.
   • The counter effect resolves: Your original spell is countered and sent to the trash.
5. Result: The spell is countered and does not resolve, but Irelia keeps the +1 Might bonus for the turn.

This is consistent with Rule 412.1.b, which notes that while a countered card is not considered to have been "played," it does not retroactively remove triggered abilities that were already placed on the chain as a result of the targeting process.