Red Tail is quite tricky boss, even I die sometime on him, but generally the following strategy works:
1. Start running ahead of you. If Red comes down, hit him until he returns on the platform and then continue (only if he is in front of you, if he is behind you just avoid the pistol)
2. Once you have reached the right end of the platform, jump on the disappearing step and then on the platform. If Red is on it at the same moment, use pistol to slow him, jump in front of him and start attacking. Beware of the time when he jumps down, he might hit you and you do not want that.
3. Once he is down, wait for him to come up. If he uses daggers, avoid them by jumping on the other end of the platform (note: if he hasn't used them, DO NOT JUMP. He will jump on the platform and you will hit him while in mid-air, thus essentially draining your life)
4. Once he gets on the platform again, repeat point 2 . Try to stay on the very end so you won't be caught by his jump. If he jumps away from you, pistol + jump in front of him and then continue on.
While this strategy is not perfect, I find it working quite well. Although, if he starts with winds (he emotes "I summon the winds!" or "Let the winds come forth!", you can consider yourself a goner.